76233_Formulae_and_Tables:Layout 1
11/12/2009
11:30
Page 1
ISBN 978-1-4064-2283-2
9 781406 422832
Foirmlí agus Táblaí
Formulae and Tables
faofa lena n-úsáid sna scrúduithe stáit
approved for use in the state examinations
BAILE ÁTHA CLIATH
ARNA FHOILSIÚ AG OIFIG AN tSOLÁTHAIR
Le ceannach díreach ó
FOILSEACHÁIN RIALTAIS,
52 FAICHE STIABHNA, BAILE ÁTHA CLIATH 2
(Teil: 01 – 6476834 nó 1890 213434; Fax 01 – 6476843)
nó trí aon díoltóir leabhar
DUBLIN
PUBLISHED BY THE STATIONERY OFFICE
To be purchased from
GOVERNMENT PUBLICATIONS,
52 ST. STEPHEN'S GREEN, DUBLIN 2.
(Tel: 01 – 6476834 or 1890 213434; Fax: 01 – 6476843)
or through any bookseller.
Praghas: €4
Price: €4
© Rialtas na hÉireann
Coimisiún na Scrúduithe Stáit
www.examinations.ie
SEC567/14-V5-Dec2014
ISBN: 978 1 4064 2862 9
Tabhair faoi deara nach
gceadaítear do chóip féin
den leabhrán seo a úsáid
sna scrúduithe stáit.
Note that you cannot use
your own copy of this booklet
in the state examinations.
Beidh cóipeanna ar fáil ón
bhfeitheoir agus ba chóir iad a
thabairt ar ais i ndeireadh
an scrúdaithe.
Copies will be available from the
superintendent and should be
returned at the end of the
examination.
Clár
Contents
Fad agus achar
8
Length and area
Achar dromchla agus toirt
10
Surface area and volume
Meastacháin ar achar
12
Area approximations
Triantánacht
13
Trigonometry
Céimseata
17
Geometry
Céimseata chomhordanáideach
18
Co-ordinate geometry
Ailgéabar
20
Algebra
Séana agus logartaim
21
Indices and logarithms
Seichimh agus sraitheanna
22
Sequences and series
Tacair agus loighic
23
Sets and logic
Calcalas
25
Calculus
Eacnamaíocht
28
Economics
Matamaitic an airgeadais
30
Financial mathematics
Staitisticí agus dóchúlacht
33
Statistics and probability
Aonaid tomhais
44
Units of measurement
Tairisigh bhunúsacha fhisiceacha
46
Fundamental physical constants
Fisic cháithníní
48
Particle physics
Meicnic
50
Mechanics
Teas agus teocht
58
Heat and temperature
Solas agus fuaim
59
Light and sound
Optaic gheoiméadrach
60
Geometric optics
Leictreachas
61
Electricity
Radaighníomhaíocht
63
Radioactivity
Ceimic
64
Chemistry
Siombailí do chainníochtaí fisiceacha coitianta
agus na haonaid ina dtomhaistear iad
65
Symbols and units of measurement
of common physical quantities
Siombailí ciorcaid leictrigh
72
Electrical circuit symbols
Na dúile
79
The elements
Tábla na núiclídí
83
Table of nuclides
Dúile, sórtáilte de réir na siombailí
91
Elements, sorted by symbol
Fad agus achar
Length and area
Seasann A iontu seo a leanas
d’achar na fíorach atá i gceist.
Comhthreomharán
In the following, A represents the
area of the shape in question.
b
h
C
A = ah
= ab sin C
Parallelogram
 a+b
A=
h
 2 
Trapezium
l = 2π r
Circle / Disc
a
b
Traipéisiam
h
a
Ciorcal / Diosca
fad l
(imlíne l)
r
A = πr 2
l
-8-
length l
(circumference l)
l
Stua / Teascóg
Arc / Sector
θ
r
when θ is in radians
 θ 
A = πr2

 360° 
when θ is in degrees
2
 θ 
l = 2π r 

 360° 
nuair is ina chéimeanna atá θ
A = 1 ah
Triantán
áit a bhfuil s =
A = 1 r 2θ
l = rθ
nuair is ina raidiain atá θ
2
c
a+b+c
2
h
a
b
C
= 1 ab sin C
2
= s( s − a)( s − b)( s − c)
-9-
Triangle
taking s =
a+b+c
2
Achar dromchla agus toirt
Surface area and volume
Seasann A iontu seo d’achar cuar
an dromchla agus seasann V do thoirt
an tsolaid atá i gceist.
In the following, A represents the
curved surface area and V represents
the volume of the solid in question.
r
A = 2 π rh
Sorcóir
h
Cón
V = πr 2 h
l
h
A = π rl
V = 1 πr 2 h
r
Sféar
Cylinder
Cone
3
A = 4π r 2
r
V = 43 π r 3
- 10 -
Sphere
A = π(r + R )l
r
Frustam cóin
l
h
Frustum of cone
(
R
Solad de thrasghearradh
aonfhoirmeach (priosma)
áit arb é B achar an bhoinn
V = 13 π h R 2 + Rr + r 2
V = Bh
h
B
Pirimid ar bhonn ar bith
áit arb é B achar an bhoinn
V = 13 Bh
h
B
- 11 -
)
Solid of uniform
cross-section (prism)
taking B as the area
of the base
Pyramid on any base
taking B as the area
of the base
Meastacháin ar achar
Area approximations
Seasann A d’achar na fíorach.
A represents the area of the shape.
y1
y2
y3
y4
…
yn
h
Riail
thraipéasóideach
Riail Simpson
áit ar corruimhir n
A≈
A≈
h
[ y1 + y n + 2( y 2 + y 3 + y 4 + + y n−1 )]
2
h
[ y1 + y n + 2( y 3 + y5 + + y n− 2 ) + 4( y 2 + y 4 + + y n−1 )]
3
- 12 -
Trapezoidal rule
Simpson’s rule
for odd n
Triantánacht
sin A
tan A =
cos A
1
sec A =
cos A
Trigonometry
(0, 1)
cos A
cot A =
sin A
1
cosec A =
sin A
(–1, 0)
cos 2 A + sin 2 A = 1
sec 2 A = 1 + tan 2 A
(cos A, sin A)
(1, 0)
A
cos(− A) = cos A
sin(− A) = − sin A
tan(− A) = − tan A
(0, –1)
Nóta: Bíonn tan A agus sec A gan sainiú nuair cos A = 0.
Bíonn cot A agus cosec A gan sainiú nuair sin A = 0.
Note: tan A and sec A are not defined when cos A = 0.
cot A and cosec A are not defined when sin A = 0.
A (céimeanna)
0°
90°
180°
270°
30°
45°
60°
A (raidiain)
0
π
2
π
3π
2
π
6
cos A
1
0
–1
0
π
4
1
π
3
1
2
sin A
0
1
0
–1
tan A
0
-
0
-
1 rad. ≈ 57.296°
- 13 -
3
2
1
2
1
2
1
2
1
3
1° ≈ 0.01745 rad.
A (degrees)
A (radians)
cos A
3
2
sin A
3
tan A
Foirmlí uillinneacha comhshuite
Compound angle formulae
cos( A + B ) = cos A cos B − sin A sin B
cos( A − B ) = cos A cos B + sin A sin B
sin( A + B ) = sin A cos B + cos A sin B
sin( A − B ) = sin A cos B − cos A sin B
tan( A + B ) =
tan A + tan B
1 − tan A tan B
tan( A − B ) =
tan A − tan B
1 + tan A tan B
Foirmlí uillinneacha dúbailte
Double angle formulae
cos 2 A = cos 2 A − sin 2 A
tan 2 A =
2 tan A
1 − tan 2 A
sin 2 A = 2 sin A cos A
cos 2 A =
1
2
(1 + cos 2 A)
cos 2 A =
1 − tan 2 A
1 + tan 2 A
sin 2 A =
1
2
(1 − cos 2 A)
sin 2 A =
2 tan A
1 + tan 2 A
- 14 -
Iolraigh a thiontú ina suimeanna agus ina ndifríochtaí
Products to sums and differences
2 cos A cos B = cos( A + B ) + cos( A − B)
2 sin A cos B = sin( A + B ) + sin( A − B)
2 sin A sin B = cos( A − B ) − cos( A + B )
2 cos A sin B = sin( A + B ) − sin( A − B )
Suimeanna agus difríochtaí a thiontú ina n-iolraigh
Sums and differences to products
cos A + cos B = 2 cos
A+ B
A−B
cos
2
2
cos A − cos B = −2 sin
A+ B
A−B
sin
2
2
sin A + sin B = 2 sin
A+ B
A− B
cos
2
2
sin A − sin B = 2 cos
A+ B
A−B
sin
2
2
- 15 -
Triantánacht an triantáin
Trigonometry of the triangle
c
A
b
B
a
1
2
achar
C
ab sin C
area
a
b
c
=
=
sin A sin B sin C
riail an tsínis
sine rule
a 2 = b 2 + c 2 − 2bc cos A
riail an chomhshínis
cosine rule
Triantán dronuilleach
Right-angled triangle
c
a
A
b
sin A =
teoirim Phíotagaráis
a
c
cos A =
b
c
c2 = a2 + b2
- 16 -
tan A =
a
b
Pythagoras’ theorem
Céimseata
Geometry
Nodaireacht
Notation
líne trí A agus B
AB
mírlíne ó A go B
[ AB ]
line through A and B
line segment from A to B
fad ó A go B
AB
distance from A to B
veicteoir ó A go B
AB
vector from A to B
veicteoir ón mbunphointe O go A
OA = a
Vector operations
Oibríochtaí le veicteoirí
nuair a thugtar na haonadveicteoirí
ceartingearacha i agus j agus
v1 = x1 i + y1 j agus v 2 = x 2 i + y 2 j
norm
iolrach scálach
vector from origin O to A
given perpendicular unit vectors i and j
and v1 = x1 i + y1 j and v 2 = x 2 i + y 2 j
2
2
v1 = x1 + y1
v1 ⋅ v 2 = x1 x 2 + y1 y 2
= v1 v 2 cos θ
- 17 -
norm
scalar product
Céimseata chomhordanáideach
Líne
Co-ordinate geometry
P ( x1 , y1 )
(0, c)
Q ( x2 , y2 )
O
fána PQ
fad [PQ]
Line
m=
y 2 − y1
x 2 − x1
PQ = ( x 2 − x1 ) 2 + ( y 2 − y1 ) 2
slope of PQ
length of [PQ]
lárphointe [PQ]
 x1 + x 2 y1 + y 2 
,


2 
 2
midpoint of [PQ]
cothromóid PQ
y − y1 = m( x − x1 )
y = mx + c
equation of PQ
achar an triantáin OPQ
pointe a roinneann [PQ]
sa chóimheas a : b
1
2
x1 y 2 − x 2 y1
area of triangle OPQ
 bx1 + ax2 by1 + ay2 
,


b+a 
 b+a
point dividing [PQ]
in the ratio a : b
- 18 -
an fad ó ( x1 , y1 ) go dtí an líne
ax + by + c = 0
uillinneacha idir dhá líne dar fánaí
m1 agus m2
distance from ( x1 , y1 ) to the line
ax1 + by1 + c
ax + by + c = 0
a2 + b2
tan θ = ±
m1 − m2
1 + m1m2
angles between two lines of
slopes m1 and m2
Ciorcal
nuair a thugtar an lárphointe
(h, k ) agus an ga r
cothromóid
tadhlaí ag ( x1 , y1 )
nuair a thugtar an chothromóid
x 2 + y 2 + 2 gx + 2 fy + c = 0
lárphointe
ga
tadhlaí ag ( x1 , y1 )
Circle
given centre (h, k ) and radius r
( x − h) 2 + ( y − k ) 2 = r 2
equation
( x − h)( x1 − h) + ( y − k )( y1 − k ) = r
2
tangent at ( x1 , y1 )
given equation x 2 + y 2 + 2 gx + 2 fy + c = 0
(− g ,− f )
centre
g2 + f 2 −c
radius
xx1 + yy1 + g ( x + x1 ) + f ( y + y1 ) + c = 0
- 19 -
tangent at ( x1 , y1 )
Ailgéabar
Algebra
fréamhacha na cothromóide cearnaí
ax 2 + bx + c = 0
x=
a b 
 leis an
inbhéarta na maitríse A = 
c d 
deitéarmanant det( A) = ad − bc ≠ 0
Teoirim de Moivre
− b ± b 2 − 4ac
2a
1  d − b


det( A)  − c a 
[r (cos θ + i sin θ )]
n
roots of the quadratic equation
ax 2 + bx + c = 0
a b 
 with
inverse of the matrix A = 
c d 
determinant det( A) = ad − bc ≠ 0
= r (cos nθ + i sin nθ ) = r e
n
An Teoirim dhéthéarmach
De Moivre’s theorem
n inθ
Binomial theorem
n
n
n
n
n
n
n
( x + y ) n = ∑   x n − r y r =   x n +   x n −1 y +   x n − 2 y 2 + +   x n −r y r + +   y n
r =0  r 
0
1
 2
r
n
comhéifeachtaí déthéarmacha
n n
n!
  = C r = C (n, r ) =
r!(n − r )!
r
- 20 -
binomial coefficients
Séana agus logartaim
Indices and logarithms
a p a q = a p+q
log a (xy ) = log a x + log a y
a x = y ⇔ log a y = x
ap
= a p −q
q
a
x
log a   = log a x − log a y
 y
log a a x = x
(a )
log a x q = q log a x
p q
( )
= a pq
1
q
q
p
q
q
a log a x = x
log a 1 = 0
a0 =1
a−p =
( )
1
log a   = − log a x
 x
1
ap
log b x =
a = a
a = ap =
( a)
q
p
(ab ) p = a p b p
p
ap
a
  = p
b
b
- 21 -
log a x
log a b
Seichimh agus sraitheanna
Sequences and series
In the following, Tn is the nth term, and
Sn is the sum of the first n terms.
Is é Tn an n ú téarma iontu seo, agus is é
Sn suim na chéad n téarma.
Seicheamh comhbhreise nó
sraith chomhbhreise
nuair:
is é a an chéad téarma, agus
is é d an chomhbhreis
Arithmetic sequence or series
Tn = a + (n − 1)d
Sn =
n
[2a + (n − 1)d ]
2
Seicheamh iolraíoch nó
sraith iolraíoch
where:
a is the first term
d is the common difference
Geometric sequence or series
Tn = ar n −1
nuair:
is é a an chéad téarma, agus
is é r an comhiolraitheoir
nuair a thugtar r < 1
Sn =
a (1 − r n )
1− r
S∞ =
a
1− r
- 22 -
where:
a is the first term
r is the common ratio
given r < 1
Tacair agus loighic
Sets and logic
Siombailí na dtacar
Set symbols
idirmhír
∩
intersection
aontas
∪
union
difríocht (lúide)
\
difference (less)
difríocht shiméadrach
∆
symmetric difference
fothacar de
⊂
is a subset of
ball de
∈
is an element of
tacar nialasach
∅
null set
Tacair uimhreacha
Number sets
= {1, 2, 3, 4, 5, 6, }
uimhreacha aiceanta
slánuimhreacha
uimhreacha cóimheasta
= { − 3, − 2, − 1, 0, 1, 2, 3, }
 p

p ∈ , q ∈ , q ≠ 0 
=
 q

réaduimhreacha
uimhreacha coimpléascacha
natural numbers
rational numbers
real numbers
{
}
= a + bi a ∈ , b ∈ , i 2 = −1
- 23 -
integers
complex numbers
Siombailí loighce
Logic symbols
AND
∧
AND
OR
∨
OR
NOT
¬
NOT
NAND
↑
NAND
NOR
↓
NOR
tugann le fios
⇒
implies
coibhéiseach le
⇔
is equivalent to
do gach
∀
for all
tá…ann
∃
there exists
a thugann
dá réir sin
Dlíthe de Morgan
Séanadh agus cainníochtóirí
yields, (infer)
∴
¬( A ∧ B ) ⇔ (¬A) ∨ (¬B )
¬( A ∨ B) ⇔ (¬A) ∧ (¬B )
¬((∀x) A( x) ) ⇔ (∃x)(¬A( x) )
¬((∃x) A( x) ) ⇔ (∀x)(¬A( x) )
- 24 -
therefore
De Morgan’s laws
Negation and quantifiers
Calcalas
Calculus
Díorthaigh
Derivatives
f (x)
f ′(x)
xn
ex
nx n −1
1
x
ex
e ax
ae ax
ax
cos x
a x ln a
− sin x
sin x
cos x
tan x
sec 2 x
1
ln x
cos −1
x
a
sin −1
x
a
tan −1
x
a
−
y = uv
Riail an toraidh
⇒
Riail an lín
y=
⇒
Product rule
dy
dv
du
=u
+v
dx
dx
dx
dy
=
dx
u
v
v
Quotient rule
du
dv
−u
dx
dx
2
v
f ( x) = u (v( x))
Cuingriail
⇒
a2 − x2
1
a2 − x2
a
2
a + x2
- 25 -
f ′( x) =
du dv
dv dx
Chain rule
Suimeálaithe
Integrals
Tá tairisigh na suimeála fágtha ar lár.
Constants of integration omitted.
f (x)
∫ f ( x)dx
f (x)
x n (n ≠ −1)
x n +1
n +1
cos 2 x
1
x
ex
ln x
cos x
ex
1 ax
e
a
ax
ln a
sin x
sin x
− cos x
tan x
ln sec x
e
ax
ax
∫ f ( x)dx
2
sin x
1
2
[x + 12 sin 2 x]
1
2
[x −
1
a −x
2
sin 2 x ]
sin −1
2
1
2
x + a2
1
2
x
a
1
x
tan −1
a
a
1
x x −a
2
- 26 -
1
x
sec −1
a
a
2
1
x2 + a2
x + x2 + a2
ln
a
1
a+x
ln
2a a − x
1
a − x2
2
1
x2 − a2
∫ udv = uv − ∫ vdu
Suimeáil
na míreanna
∫ f ( x)dx
f (x)
ln
x + x2 − a2
a
Integration by parts
Atriall Newton-Raphson
x n +1 = x n −
f ( xn )
f ′( x n )
Newton-Raphson iteration
Sraith Taylor agus a mar lárphointe
Taylor series with centre a
f (a + x) = f (a ) + f ′(a ) x +
f ′′(a ) 2
f ( r ) (a) r
x ++
x +
2!
r!
Sraith Maclaurin
Maclaurin series
f ( x) = f (0) + f ′(0) x +
f ′′(0) 2
f ( r ) (0) r
x +
x + +
2!
r!
Toirt solaid imrothlaithe timpeall ar an x-ais
Volume of solid of revolution about x-axis
V=
∫
x =b
π y 2 dx
x=a
- 27 -
Eacnamaíocht
Economics
Leaisteachas
Elasticity
Iontu seo a leanas,
P = praghas, Q = cainníocht, Y = ioncam,
tagraíonn foscript 1 agus 2 don am
roimh an athrú agus ina dhiaidh,
agus seasann A agus B do na hearraí A agus B.
In the following,
P = price, Q = quantity, Y = income,
subscripts 1 and 2 refer to
before and after change,
A and B refer to goods A and B.
praghasleaisteachas an éilimh
∆Q P1 + P2
×
∆P Q1 + Q2
price elasticity of demand
ioncamleaisteachas an éilimh
∆Q Y1 + Y2
×
∆Y Q1 + Q2
income elasticity of demand
trasleaisteachas an éilimh
praghasleaisteachas an tsoláthair
∆Q A P1, B + P2, B
×
∆PB Q1, A + Q2, A
∆Q P1 + P2
×
∆P Q1 + Q2
- 28 -
cross price elasticity of demand
price elasticity of supply
Cothromóid OTI
Y = olltáirgeacht intíre
C = caiteachas ar thomhaltas
I = caiteachas ar infheistíocht
G = ceannacháin rialtais
( X − M ) = glanluach easpórtálacha
Y = C + I + G + (X − M )
Iolraitheoirí
Iontu seo a leanas,
MPC = claonadh imeallach chun tomhaltais
MPS = claonadh imeallach chun coigilte
MPM = claonadh imeallach chun iompórtála
MPT = claonadh imeallach chun cáin a íoc
Nóta: MPS = 1 − MPC
geilleagar iata gan earnáil rialtais
GDP equation
Y = gross domestic product
C = consumption expenditure
I = investment expenditure
G = government purchases
( X − M ) = net exports
Multipliers
In the following,
MPC = marginal propensity to consume
MPS = marginal propensity to save
MPM = marginal propensity to import
MPT = marginal propensity to pay tax
Note: MPS = 1 − MPC
1
MPS
geilleagar oscailte gan earnáil rialtais
1
MPS + MPM
geilleagar oscailte le hearnáil rialtais
1
MPS + MPM + MPT
- 29 -
closed economy with no government sector
open economy with no government sector
open economy with government sector
Matamaitic an airgeadais
Financial mathematics
Iontu seo a leanas, is é t an fad ama ina bhlianta
agus is é i an ráta bliantúil úis, dímheasa nó fáis,
agus é sloinnte mar dheachúil nó mar chodán (ionas
go seasann i = 0.08 do ráta 8%, mar shampla)*.
In all of the following, t is the time in years and i is
annual rate of interest, depreciation or growth,
expressed as a decimal or fraction (so that, for
example, i = 0.08 represents a rate of 8%)*.
Ús iolraithe
F = luach deiridh, P = príomhshuim
F = P (1 + i )
Luach láithreach
P = luach láithreach, F = luach deiridh
P=
Dímheas
– modh an chomhardaithe laghdaithigh
F = luach déanach, P = luach tosaigh
F = P (1 − i )
Dímheas
– an modh dronlíneach
A = méid an dímheasa bhliantúil
P = luach tosaigh, S = dramhluach
t = saolré eacnamaíoch fhónta
t
Present value
P = present value, F = final value
F
(1 + i )
t
t
A=
P−S
t
*Bíonn feidhm ag na foirmlí sin freisin nuair a bhítear
ag athiolrú i gceann eatraimh chothroma seachas blianta. Sa
chás sin, déantar t a thomhas sa tréimhse chuí ama, agus is é i
an ráta don tréimhse.
Compound interest
F = final value, P = principal
Depreciation
– reducing balance method
F = later value, P = initial value
Depreciation
– straight line method
A = annual depreciation amount
P = initial value, S = scrap value
t = useful economic life
*The formulae also apply when compounding at
equal intervals other than years. In such cases, t is
measured in the relevant periods of time, and i is
the period rate.
- 30 -
Amúchadh – morgáistí agus iasachtaí
(aisíocaíochtaí cothroma i gceann eatraimh
chothroma)
A = méid na haisíocaíochta bliantúla
P = príomhshuim
Amortisation – mortgages and loans
(equal repayments at equal intervals)
i(1 + i)
(1 + i ) t − 1
t
A= P
Ráta céatadánach bliantúil (RCB)
– foirmle reachtúil
Is ionann an RCB agus luach i (agus é sloinnte ina
chéatadán) nuair is ionann suim luachanna reatha
na n-airleacan uile agus suim luachanna reatha na
n-aisíocaíochtaí uile. Is é sin, luach i áit a bhfuil:
N
Annual percentage rate (APR)
– statutory formula
The APR is the value of i (expressed as a percentage)
for which the sum of the present values of all
advances is equal to the sum of the present values of
all repayments. That is, the value of i for which:
n
∑ (1 + i) = ∑ (1 + i)
k =1
nuair:
is é N líon na n-airleacan
is é n líon na n-aisíocaíochtaí
is é Ak méid an airleacain k
is é Rj méid na haisíocaíochta j
is é Tk an fad ama ina bhlianta go dtí airleacan k
is é tj an fad ama ina bhlianta go dtí aisíocaíocht j
A = annual repayment amount
P = principal
Ak
Tk
- 31 -
j =1
Rj
tj
where:
N is the number of advances
n is the number of repayments
Ak is the amount of advance k
Rj is the amount of repayment j
Tk is the time in years to advance k
tj is the time in years to repayment j
Tréimhse eile iolraithe a thiontú
ina ráta bliantúil
Converting to annual rate from other
compounding period
m
r

i = 1 +  − 1
 m
nuair
is é i an ráta bliantúil iarbhír (mar dheachúil)
is é r an ráta bliantúil ainmniúil (mar dheachúil)
is é m líon na dtréimhsí athiolraithe in aon bhliain
amháin
where
i is the actual annual rate (as a decimal)
r is the nominal annual rate (as a decimal)
m is the number of compounding periods in one year
Athiolrú leanúnach
Continuous compounding
F = Pe
nuair
is é F an luach deiridh
is é P an phríomhshuim
is é r an ráta bliantúil ainmniúil
is é i an ráta bliantúil iarbhír
rt
i = er −1
r = log e (1 + i )
- 32 -
where
F is the final value
P is the principal
r is the nominal annual rate
i is the actual annual rate
Staitisticí agus dóchúlacht
Statistics and probability
An Meán
Mean
Σx
n
Σfx
µ=
Σf
µ=
ó liosta de n uimhir
ó thábla minicíochta
An Diall caighdeánach
ó liosta de n uimhir
ó thábla minicíochta
an meán
an diall caighdeánach
from frequency table
Standard deviation
σ=
σ=
Σ( x − µ ) 2
n
from list of n numbers
Σ f (x − µ) 2
Σf
from frequency table
Dáiltí dóchúlachta
an dáileadh déthéarmach
from list of n numbers
Probability distributions
n
P ( X = r ) =   p r q n − r
r
r = 0… n
µ = np
σ = npq
- 33 -
binomial distribution
mean
standard deviation
dáileadh Poisson
λr
P ( X = r ) = e −λ
r = 0, 1, 2, …
µ =λ
an meán
an diall caighdeánach
an dáileadh normalach (dáileadh Gauss)
an dáileadh normalach caighdeánach
r!
mean
standard deviation
σ= λ
f (X ) =
σ 2π
f (Z ) =
z=
foirmle an chaighdeánaithe
−
1
( X −µ )2
e
2π
x−µ
σ
Sampláil
meastachán ar dhiall caighdeánach
an daonra ó sampla
earráid chaighdeánach an mheáin
earráid chaighdeánach na comhréire
2σ 2
1
− Z2
e 2
1
Poisson distribution
normal (Gaussian) distribution
standard normal distribution
standardising formula
Sampling
s=
Σ( x − x ) 2
n −1
σX =
σPˆ =
σ
n
p(1 − p )
n
- 34 -
estimate of population standard
deviation from sample
standard error of the mean
standard error of the proportion
Tástáil hipitéisí
Hypothesis testing
x−µ
 σ 


 n
z=
z-thástáil aon sampla
t=
t-thástáil aon sampla
z-thástáil dhá shampla
x−µ
;
ν = n −1
 s 


 n
x1 − x 2
z=
σ 12
n1
t-thástáil
dhá shampla
(comhthiomsaithe)
t=
x1 − x 2
2
s2 =
1
1 ;
s
+
n1 n 2
tástáil χ 2
ar fheabhas na hoiriúnachta
k catagóir, m paraiméadar mheasta
suntasacht chomhéifeacht
an chomhchoibhnis (Pearson)
k
χ =∑
2
i =1
t=
one-sample z-test
+
one-sample t-test
two-sample z-test
σ 22
n2
2
(n1 − 1) s1 + (n 2 − 1) s 2
;
n1 + n 2 − 2
(oi − ei ) 2
;
ei
r n−2
1− r2
;
- 35 -
ν = n1 + n 2 − 2
ν = k −1− m
ν =n−2
two-sample t-test
(pooled)
χ 2 goodness-of-fit test
k categories,
m estimated parameters
significance of correlation
coefficient (Pearson)
Dóchúlachtaí don
dáileadh normalach caighdeánach
Probabilities for the
standard normal distribution
I gcás z a thugtar, faightear ón tábla
P (Z ≤ z ) =
1
2π
∫
z
For a given z, the table gives
1
− t2
e 2 dt
P(Z ≤ z ) =
−∞
-3
-2
-1
0
1 z
2
1
2π
∫
z
1
− t2
e 2 dt
−∞
3
z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.5000
.5040
.5080
.5120
.5160
.5199
.5239
.5279
.5319
.5359
0.1
0.2
0.3
0.4
0.5398
0.5793
0.6179
0.6554
.5438
.5832
.6217
.6591
.5478
.5871
.6255
.6628
.5517
.5910
.6293
.6664
.5557
.5948
.6331
.6700
.5596
.5987
.6368
.6736
.5636
.6026
.6406
.6772
.5675
.6064
.6443
.6808
.5714
.6103
.6480
.6844
.5753
.6141
.6517
.6879
0.5
0.6915
.6950
.6985
.7019
.7054
.7088
.7123
.7157
.7190
.7224
0.6
0.7
0.8
0.9
0.7257
0.7580
0.7881
0.8159
.7291
.7611
.7910
.8186
.7324
.7642
.7939
.8212
.7357
.7673
.7967
.8238
.7389
.7704
.7995
.8264
.7422
.7734
.8023
.8289
.7454
.7764
.8051
.8315
.7486
.7794
.8078
.8340
.7517
.7823
.8106
.8365
.7549
.7852
.8133
.8389
1.0
0.8413
.8438
.8461
.8485
.8508
.8531
.8554
.8577
.8599
.8621
- 36 -
an dáileadh normalach (ar lean)
normal distribution (continued)
z
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
1.1
1.2
1.3
1.4
0.8643
0.8849
0.9032
0.9192
.8665
.8869
.9049
.9207
.8686
.8888
.9066
.9222
.8708
.8907
.9082
.9236
.8729
.8925
.9099
.9251
.8749
.8944
.9115
.9265
.8770
.8962
.9131
.9279
.8790
.8980
.9147
.9292
.8810
.8997
.9162
.9306
.8830
.9015
.9177
.9319
1.5
0.9332
.9345
.9357
.9370
.9382
.9394
.9406
.9418
.9429
.9441
1.6
1.7
1.8
1.9
0.9452
0.9554
0.9641
0.9713
.9463
.9564
.9649
.9719
.9474
.9573
.9656
.9726
.9484
.9582
.9664
.9732
.9495
.9591
.9671
.9738
.9505
.9599
.9678
.9744
.9515
.9608
.9686
.9750
.9525
.9616
.9693
.9756
.9535
.9625
.9699
.9761
.9545
.9633
.9706
.9767
2.0
0.9772
.9778
.9783
.9788
.9793
.9798
.9803
.9808
.9812
.9817
2.1
2.2
2.3
2.4
0.9821
0.9861
0.9893
0.9918
.9826
.9864
.9896
.9920
.9830
.9868
.9898
.9922
.9834
.9871
.9901
.9925
.9838
.9875
.9904
.9927
.9842
.9878
.9906
.9929
.9846
.9881
.9909
.9931
.9850
.9884
.9911
.9932
.9854
.9887
.9913
.9934
.9857
.9890
.9916
.9936
2.5
0.9938
.9940
.9941
.9943
.9945
.9946
.9948
.9949
.9951
.9952
2.6
2.7
2.8
2.9
0.9953
0.9965
0.9974
0.9981
.9955
.9966
.9975
.9982
.9956
.9967
.9976
.9982
.9957
.9968
.9977
.9983
.9959
.9969
.9977
.9984
.9960
.9970
.9978
.9984
.9961
.9971
.9979
.9985
.9962
.9972
.9979
.9985
.9963
.9973
.9980
.9986
.9964
.9974
.9981
.9986
3.0
0.9987
.9987
.9987
.9988
.9988
.9989
.9989
.9989
.9990
.9990
- 37 -
Dáileadh chí-chearnaithe
luachanna criticiúla tástála aonfhoircní
Nuair a thugtar A, faightear ón tábla
an luach ar k mar a bhfuil P ( X > k ) = A ,
áit a leanann X dáileadh chí-chearnaithe
a bhfuil ν céim saoirse aige.
Chi-squared distribution
one-tailed critical values
Given A, the table gives the value of
k for which P ( X > k ) = A , where X
follows a chi-squared distribution
with ν degrees of freedom.
A
k
A
ν
1
2
3
4
5
6
7
8
9
10
11
12
13
14
0.995
0.99
0.975
0.95
0.05
0.025
0.01
0.005
0.0000
0.0100
0.0717
0.2070
0.4117
0.6757
0.9893
1.3444
1.7349
2.1559
2.6032
3.0738
3.5650
4.0747
0.0002
0.0201
0.1148
0.2971
0.5543
0.8721
1.2390
1.6465
2.0879
2.5582
3.0535
3.5706
4.1069
4.6604
0.0010
0.0506
0.2158
0.4844
0.8312
1.2373
1.6899
2.1797
2.7004
3.2470
3.8157
4.4038
5.0088
5.6287
0.0039
0.1026
0.3518
0.7107
1.1455
1.6354
2.1673
2.7326
3.3251
3.9403
4.5748
5.2260
5.8919
6.5706
3.8415
5.9915
7.8147
9.4877
11.070
12.592
14.067
15.507
16.919
18.307
19.675
21.026
22.362
23.685
5.0239
7.3778
9.3484
11.143
12.833
14.449
16.013
17.535
19.023
20.483
21.920
23.337
24.736
26.119
6.6349
9.2103
11.345
13.277
15.086
16.812
18.475
20.090
21.666
23.209
24.725
26.217
27.688
29.141
7.8794
10.597
12.838
14.860
16.750
18.548
20.278
21.955
23.589
25.188
26.757
28.300
29.819
31.319
- 38 -
dáileadh chí-chearnaithe (ar lean)
A
chi-squared distribution (continued)
ν
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0.995
0.99
0.975
0.95
0.05
0.025
0.01
0.005
4.6009
5.1422
5.6972
6.2648
6.8440
7.4338
8.0337
8.6427
9.2604
9.8862
10.520
11.160
11.808
12.461
13.121
13.787
5.2293
5.8122
6.4078
7.0149
7.6327
8.2604
8.8972
9.5425
10.196
10.856
11.524
12.198
12.879
13.565
14.256
14.953
6.2621
6.9077
7.5642
8.2307
8.9065
9.5908
10.283
10.982
11.689
12.401
13.120
13.844
14.573
15.308
16.047
16.791
7.2609
7.9616
8.6718
9.3905
10.117
10.851
11.591
12.338
13.091
13.848
14.611
15.379
16.151
16.928
17.708
18.493
24.996
26.296
27.587
28.869
30.144
31.410
32.671
33.924
35.172
36.415
37.652
38.885
40.113
41.337
42.557
43.773
27.488
28.845
30.191
31.526
32.852
34.170
35.479
36.781
38.076
39.364
40.646
41.923
43.195
44.461
45.722
46.979
30.578
32.000
33.409
34.805
36.191
37.566
38.932
40.289
41.638
42.980
44.314
45.642
46.963
48.278
49.588
50.892
32.801
34.267
35.718
37.156
38.582
39.997
41.401
42.796
44.181
45.559
46.928
48.290
49.645
50.993
52.336
53.672
40
50
60
70
80
90
100
20.707
27.991
35.534
43.275
51.172
59.196
67.328
22.164
29.707
37.485
45.442
53.540
61.754
70.065
24.433
32.357
40.482
48.758
57.153
65.647
74.222
26.509
34.764
43.188
51.739
60.391
69.126
77.929
55.758
67.505
79.082
90.531
101.88
113.15
124.34
59.342
71.420
83.298
95.023
106.63
118.14
129.56
63.691
76.154
88.379
100.43
112.33
124.12
135.81
66.766
79.490
91.952
104.21
116.32
128.30
140.17
- 39 -
Student’s t-distribution
one-tailed critical values
t-dháileadh Student
luachanna criticiúla tástála aonfhoircní
Nuair a thugtar A, faightear ón tábla an luach
ar k mar a bhfuil P (T > k ) = A,
Given A, the table gives the value
of k for which P (T > k ) = A,
A
áit a leanann T, t-dháileadh a bhfuil
ν céim saoirse aige.
A
where T follows a t-distribution
with ν degrees of freedom.
k
0.1
0.05
0.025
0.01
0.005
0.001
0.0005
0.0001
0.00005
1
2
3
4
3.078
6.314
12.71
31.82
63.66
318.3
636.6
3183
6366
1.886
1.638
1.533
2.920
2.353
2.132
4.303
3.182
2.776
6.965
4.541
3.747
9.925
5.841
4.604
22.33
10.21
7.173
31.60
12.92
8.610
70.70
22.20
13.03
99.99
28.00
15.54
5
1.476
2.015
2.571
3.365
4.032
5.893
6.869
9.678
11.18
6
7
8
9
1.440
1.415
1.397
1.383
1.943
1.895
1.860
1.833
2.447
2.365
2.306
2.262
3.143
2.998
2.896
2.821
3.707
3.499
3.355
3.250
5.208
4.785
4.501
4.297
5.959
5.408
5.041
4.781
8.025
7.063
6.442
6.010
9.082
7.885
7.120
6.594
10
1.372
1.812
2.228
2.764
3.169
4.144
4.587
5.694
6.211
11
12
13
14
1.363
1.356
1.350
1.345
1.796
1.782
1.771
1.761
2.201
2.179
2.160
2.145
2.718
2.681
2.650
2.624
3.106
3.055
3.012
2.977
4.025
3.930
3.852
3.787
4.437
4.318
4.221
4.140
5.453
5.263
5.111
4.985
5.921
5.694
5.513
5.363
ν
- 40 -
t-dháileadh Student (ar lean)
A
Student’s t-distribution (continued)
ν
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0.1
0.05
0.025
0.01
0.005
0.001
0.0005
0.0001
0.00005
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
3.733
3.686
3.646
3.610
3.579
3.552
3.527
3.505
3.485
3.467
3.450
3.435
3.421
3.408
3.396
3.385
4.073
4.015
3.965
3.922
3.883
3.850
3.819
3.792
3.768
3.745
3.725
3.707
3.689
3.674
3.660
3.646
4.880
4.790
4.715
4.648
4.590
4.539
4.492
4.452
4.416
4.382
4.352
4.324
4.299
4.276
4.254
4.234
5.239
5.134
5.043
4.966
4.899
4.838
4.785
4.736
4.694
4.654
4.619
4.587
4.556
4.531
4.505
4.482
40
50
60
80
100
1.303
1.299
1.296
1.292
1.290
1.684
1.676
1.671
1.664
1.660
2.021
2.009
2.000
1.990
1.984
2.423
2.403
2.390
2.374
2.364
2.704
2.678
2.660
2.639
2.626
3.307
3.261
3.232
3.195
3.174
3.551
3.496
3.460
3.416
3.390
4.094
4.014
3.962
3.899
3.861
4.321
4.228
4.169
4.095
4.054
∞
1.282
1.645
1.960
2.326
2.576
3.090
3.290
3.719
3.891
- 41 -
Mearthástáil Tukey (foirm achomair)
Leibhéal suntasachta
Luach criticiúil áireamh na bhfoirceann
Comhéifeacht Spearman
do chomhchoibhneas na rang-ord
luachanna criticiúla tástála aonfhoircní
n
5%
2.5%
0.900
1.000
5
0.829
0.886
6
0.714
0.786
7
0.643
0.738
8
0.600
0.700
9
0.564
0.648
10
0.536
0.618
11
0.503
0.587
12
0.484
0.560
13
0.464
0.538
14
0.446
0.521
15
0.429
0.503
16
Tukey quick test (compact form)
5%
1%
0.1%
7
10
13
n
17
18
19
20
21
22
23
24
25
26
27
28
5%
0.414
0.401
0.391
0.380
0.370
0.361
0.353
0.344
0.337
0.331
0.324
0.318
- 42 -
2.5%
0.488
0.472
0.460
0.447
0.436
0.425
0.416
0.407
0.398
0.390
0.383
0.375
Significance level
Critical value of tail-count
Spearman’s rank-order
correlation coefficient
one-tailed critical values
n
5%
2.5%
0.312
0.368
29
0.306
0.362
30
0.301
0.356
31
0.296
0.350
32
0.291
0.345
33
0.287
0.340
34
0.283
0.335
35
0.279
0.330
36
0.275
0.325
37
0.271
0.321
38
0.267
0.317
39
0.264
0.313
40
Mann-Whitney U-test
two-tailed 5% critical values
U-thástáil Mann-Whitney
luachanna criticiúla tástála défhoircní ar 5%
A value of U less than or equal to the value in the
table indicates a significant difference.
Má fhaightear luach ar U atá níos lú ná an luach sa tábla
nó cothrom leis, tá difríocht shuntasach i gceist.
2
-
3
-
4
0
5
0
1
2
U = min{U 1 , U 2 }
U 1 = R1 −
n1 ( n1 + 1)
,
2
6
1
2
3
5
7
1
3
5
6
8
8
0
2
4
6
8
10
13
9
0
2
4
7
10
12
15
17
10
0
3
5
8
11
14
17
20
23
11
0
3
6
9
13
16
19
23
26
30
n1
12
1
4
7
11
14
18
22
26
29
33
37
áit a bhfuil
where
U 2 = R2 −
n 2 ( n2 + 1)
2
- 43 -
13
1
4
8
12
16
20
24
28
33
37
41
45
14
1
5
9
13
17
22
26
31
36
40
45
50
55
15
1
5
10
14
19
24
29
34
39
44
49
54
59
64
16
1
6
11
15
21
26
31
37
42
47
53
59
64
70
75
17
2
6
11
17
22
28
34
39
45
51
57
63
67
75
81
87
18
2
7
12
18
24
30
36
42
48
55
61
67
74
80
86
93
99
19
2
7
13
19
25
32
38
45
52
58
65
72
78
85
92
99
106
113
20
2
8
14
20
27
34
41
48
55
62
69
76
83
90
98
105
112
119
127
n2
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Aonaid tomhais
Units of measurement
Na bunaonaid
Tá Córas Idirnáisiúnta na nAonad (Système International
d’Unités) bunaithe ar sheacht mbunchainníocht a nglactar
leis iad a bheith neamhspleách ar a chéile.
Is iad seo a leanas na bunaonaid:
Base units
The International System of Units (Système
International d’Unités) is founded on seven base
quantities, which are assumed to be mutually
independent. These base units are:
SI base
unit
Base quantity
m
metre
length (l)
kg
kilogram
mass (m)
s
second
time (t)
aimpéar
A
ampere
electric current (I)
teocht (T )
ceilvin
K
kelvin
temperature (T)
méid substainte (n)
mól
mol
mole
amount of substance (n)
déine lonrachais (Iν)
caindéala
cd
candela
luminous intensity (Iν)
Bunchainníocht
Bunaonad SI
fad (l)
méadar
mais (m)
cileagram
am (t)
soicind
sruth leictreach (I )
Siombail an aonaid
Symbol for unit
Derived units
A derived unit is a unit which can be expressed in
terms of base units and is given a unique name,
e.g. newton (N) = kg m s–2.
Aonaid dhíortha
Is é is aonad díortha ann aonad is féidir a shloinneadh
i dtéarmaí na mbunaonad agus a dtugtar ainm uathúil
air, e.g. niútan (N) = kg m s–2.
- 44 -
Réimíreanna
Baintear leas as réimíreanna chun iolraithe agus
fo-iolraithe deachúlacha d’aonaid SI a dhéanamh.
Is iad seo na réimíreanna coitianta:
Réimír
yota-, yotaizeitea-, zeiti-
Fachtóir Siombail
Factor
Symbol
24
10
Y
1021
Prefixes
Prefixes are used to form decimal multiples and
submultiples of SI units. The common prefixes are:
Prefix
Réimír
yotta
yochta-, yochtai-
zetta
zeiptea-, zeipti-
Z
Fachtóir Siombail
Factor
Symbol
–24
10
y
Prefix
yocto
10–21
z
zepto
–18
a
atto
eicsea-, eicsi-
10
18
E
exa
ata-, atai
10
peitea-, peiti-
1015
P
peta
feimtea-, feimti-
10–15
f
femto
teirea-, teiri-
1012
T
tera
picea-, pici-
10–12
p
pico
gigea-, gigi-
10
9
G
giga
nana-, nanai-
10
–9
n
nano
meigea-, meigi-
106
M
mega
micrea-, micri-
10–6
µ
micro
cilea-, cili-
103
k
kilo
millea-, milli-
10–3
m
milli
–2
2
heictea-, heicti-
10
h
hecto
ceintea-, ceinti-
10
c
centi
deaca-, deacai-
101
da
deka
deicea-, deici-
10–1
d
deci
Cónasctar siombail réimíre le siombail bunaonaid
chun siombail nua aonaid a dhéanamh,
e.g. ciliméadar (km), micreashoicind (µs).
The symbol for a prefix is combined with the symbol
for the base unit to form a new unit symbol,
e.g. kilometre (km), microsecond (µs).
- 45 -
Tairisigh bhunúsacha fhisiceacha
Tairiseach
Fundamental physical constants
Siombail
Symbol
Luach
Value
Constant
mais alfa-cháithnín
mα
6.644 6565 × 10–27 kg
alpha particle mass
tairiseach Avogadro
NA
6.022 1415 × 1023 mol–1
Avogadro constant
tairiseach Boltzmann
k
1.380 6505 × 10–23 J K–1
Boltzmann constant
mais leictreoin
me
9.109 3826 × 10–31 kg
electron mass
leictreonvolta
eV
1.602 176 53 × 10–19 J
electron volt
lucht leictreonach
e
1.602 176 53 × 10–19 C
electronic charge
tairiseach Faraday
F
96 485.3383 C mol–1
Faraday constant
tairiseach na himtharraingthe
G
6.6742 × 10–11 m3 kg–1 s–2
mais neodróin
mn
1.674 927 28 × 10–27 kg
- 46 -
gravitational constant
neutron mass
Tairiseach
Siombail
Symbol
Luach
Value
Constant
tréscaoilteacht an tsaorspáis
µ0
4π × 10–7 H m–1
ceadaíocht an tsaorspáis
ε0
8.854 187 817 × 10–12 F m–1
tairiseach Planck
h
6.626 0693 × 10–34 J s
mais phrótóin
mp
1.672 621 71 × 10–27 kg
cóimheas maise prótóin is
leictreoin
mp
me
1836.182 672 16
luas an tsolais in vacuo
c0
2.997 924 58 × 108 m s–1
aonad maise adamhaí aontaithe
u
1.660 5402 × 10–27 kg
unified atomic mass unit
tairiseach uilíoch gáis
R
8.314 472 J K–1 mol–1
universal gas constant
- 47 -
permeability of free space
permittivity of free space
Planck constant
proton mass
proton-electron mass ratio
speed of light in vacuo
Fisic cháithníní
Aicme
ainm
Leaptóin
leictreon
leictreon-neoidríonó
muón
muón-neoidríonó
tó
tó-neoidríonó
Méasóin
pí-mhéasón
K-mhéasón
Baróin
prótón
neodrón
lambda
sigme
xí
óimige
Particle physics
Mais / Mass
Siombail
Symbol
(i gcoibhneas le mais leictreoin)
(relative to mass of electron)
e
νe
µ
νµ
τ
ντ
1
< 4 × 10–6
2.07 × 102
< 4 × 10–6
3.48 × 103
< 4 × 10–6
cobhsaí / stable
cobhsaí / stable
1.52 × 10–6 s
cobhsaí / stable
2.01 × 10–13 s
cobhsaí / stable
π+ π –
πo
+
K K–
Ko
273
264
966
974
1.80 × 10–8 s
5.82 × 10–17 s
8.58 × 10–9 s

p
n
Λo
Σ+
Σ–
Σo
Ξ–
Ξo
Ω–
1836
1839
2183
2328
2343
2334
2586
2573
3272
cobhsaí / stable
6.14 × 102 s
1.82 × 10–10 s
5.56 × 10–11 s
1.02 × 10–10 s
5.13 × 10–20 s
1.14 × 10–10 s
2.01 × 10–10 s
5.69 × 10–11 s
- 48 -
Leath-ré
Half-life
Class
name
Leptons
electron
electron neutrino
muon
muon neutrino
tau
tau neutrino
Mesons
pi meson
K meson
Baryons
proton
neutron
lambda
sigma
xi
omega
siombail
symbol
lucht
charge
uaschuarc
u
2
3
íoschuarc
d
briochtchuarc
c
cuarc aduain
s
barrchuarc
t
bunchuarc
b
cuarc
−
1
3
2
3
−
1
3
2
3
−
- 49 -
1
3
quark
up
down
charm
strange
top
bottom
Tugtar liosta aibítreach de na siombailí a
úsáidtear sna foirmlí seo a leanas agus an bhrí
atá leo sa comhthéacs cuí ar leathanach 65.
An alphabetical list of the symbols used in
the following formulae and their meaning
in the relevant context is given on page 65.
Meicnic
fórsa agus luasghéarú
Gluaisne líneach faoi luasghéarú
tairiseach
Mechanics
F = ma
v = u + at
force and acceleration
Linear motion with constant
acceleration
s = ut + 12 at 2
v 2 = u 2 + 2as
u + v
s=
t
 2 
Gluaisne choibhneasta
díláithriú coibhneasta
treoluas coibhneasta
luasghéarú coibhneasta
Relative motion
s BC = s B − sC
vBC = vB − vC
a BC = a B − aC
- 50 -
relative displacement
relative velocity
relative acceleration
Imbhuailtí
Collisions
móiminteam cáithnín
dlí turgnamhach Newton
imchoimeád an mhóimintim
ríog
momentum of a particle
mv
v1 – v2 = – e(u1 – u2)
Newton’s experimental law
m1 u 1 + m2 u 2 = m1 v 1 + m2 v 2
conservation of momentum
∫
I = F dt = mv − mu
Gluaisne i gciorcal
Motion in a circle
s
r
uillinn ina raidiain
θ=
treoluas uilleach
ω=
treoluas líneach agus uilleach
v = rω
luasghéarú láraimsitheach
fórsa láraimsitheach
impulse
θ
angular velocity
t
a = rω 2=
2
F = mrω =
- 51 -
angle in radians
linear and angular velocity
v2
r
mv 2
r
centripetal acceleration
centripetal force
Meáchanláir
leathsféar soladach, ga r,
fad slí ó lárphointe an leathsféir
go dtí an meáchanlár
Centres of gravity
solid hemisphere, radius r
3
8
r
distance from centre of hemisphere
to centre of gravity
1
2
r
distance from centre of hemisphere
to centre of gravity
sliogán leathsféarach, ga r,
fad slí ó lárphointe an leathsféir
go dtí an meáchanlár
hemispherical shell, radius r
solid right circular cone, height h
dronchón ciorclach soladach, airde h
fad slí ó bhonn an chóin
go dtí an meáchanlár
1
4
distance from base of cone
to centre of gravity
h
lann thriantánach
1
3
triangular lamina
1
3
ón mbonn feadh na meánlíne
foirm chomhordanáideach
stua, ga r, stua-uillinn 2θ
fad slí ó lárphointe an chiorcail
go dtí meáchanlár an stua
teascóg diosca, ga r, stua-uillinn 2θ
fad slí ó lárphointe an chiorcail
go dtí meáchanlár na teascóige
 x1 + x 2 + x3 y1 + y 2 + y 3 
,


3
3


r sin θ
θ
2r sin θ
3θ
- 52 -
from base along median
co-ordinate form
arc, radius r, arc-angle 2θ
distance from centre of circle
to centre of gravity of arc
sector of disc, radius r, arc-angle 2θ
distance from centre of circle
to centre of gravity of sector
Móimintí táimhe
Moments of inertia
slat aonfhoirmeach, fad 2l
uniform rod, length 2l
timpeall aise trí lárphointe ingearach leis an tslat
1
3
ml 2
about axis through centre perpendicular to rod
timpeall aise ag foirceann amháin ingearach
leis an tslat
4
3
ml 2
about axis at one end perpendicular to rod
1
2
mr 2
1
4
mr 2
about diameter
mr 2
about axis through centre perpendicular to hoop
1
2
mr 2
about diameter
2
5
mr 2
diosca aonfhoirmeach, ga r
timpeall aise trí lárphointe ingearach leis an diosca
timpeall trastomhais
fonsa aonfhoirmeach, ga r
timpeall aise trí lárphointe ingearach leis an bhfoinse
timpeall trastomhais
sféar soladach aonfhoirmeach, ga r
timpeall trastomhais
uniform disc, radius r
about axis through centre perpendicular to disc
uniform hoop, radius r
uniform solid sphere, radius r
about diameter
teoirim na n-aiseanna
comhthreomhara
I b = I c + md 2
parallel axis theorem
teoirim na n-aiseanna ingearacha
Iz = Ix + Iy
perpendicular axis theorem
- 53 -
Coirp rothlacha
Rotating bodies
L = Iω = rmv
angular momentum
móimint fórsa
M = Fd
moment of a force
torc cúpla
T = Fd
torque of a couple
dara dlí Newton don rothlú
T =
dL
dt
Newton’s 2nd law for rotation
fuinneamh cinéiteach rothlach
E = 12 Iω 2
móiminteam uilleach
Gluaisne armónach shimplí
rotational kinetic energy
Simple harmonic motion
2
a=–ωs
T=
1
f
=
2π
ω
s = A sin (ω t + α )
2
2
v = ω ( A 2 – s 2)
luascadán simplí
comhluascadán
T = 2π
T = 2π
- 54 -
l
g
I
mgh
simple pendulum
compound pendulum
Fuinneamh agus obair
obair
cumhacht
Energy and work
W = Fs =
P=
∫ Fds
W
= Fv
t
work
power
Po × 100
Pi
percentage efficiency
fuinneamh poitéinsiúil (imtharraingthe)
Ep = mgh
potential energy (gravitational)
fuinneamh cinéiteach
Ek =
céatadán éifeachtachta
prionsabal imchoimeád an fhuinnimh
(faoi fhórsaí meicniúla imchoimeádacha)
coibhéis mhaise is fuinnimh
1
2
mv 2
∆E p + ∆E k = 0
E = mc 2
- 55 -
kinetic energy
principle of conservation of energy
(under conservative mechanical forces)
mass-energy equivalence
Imtharraingt
dlí imtharraingthe Newton
meáchan
luasghéarú de bharr
na domhantarraingthe
neart réimse imtharraingthe
peiriad satailíte
Gravitation
Gm1m2
d2
F=
W = mg = Vρ g
g=
weight
GM
d2
acceleration due to gravity
F
m
gravitational field strength
g=
T2 =
Newton’s law of gravitation
4π 2 R 3
GM
- 56 -
period of a satellite
Fórsaí agus ábhair
Forces and materials
dlí Hooke
F = − ks
strus
σ=
F
A
stress
straidhn
ε=
∆l
l
strain
modal Young
E=
σ
ε
Young’s modulus
dlús
ρ=
m
V
density
comhéifeacht na frithchuimilte
µ=
F
R
coefficient of friction
p=
F
A
pressure
brú
Hooke’s law
brú i leacht
p = ρgh
pressure in a fluid
sá ar dhromchla plánach tumtha
T = A pC
thrust on an immersed plane surface
dlí Boyle
p∝
- 57 -
1
V
Boyle’s law
Teas agus teocht
Heat and temperature
θ/ ˚C = T/ K – 273.15
teocht Celsius
Celsius temperature
an fuinneamh a theastaíonn chun
teocht a athrú
∆ E = mc ∆ θ
∆E = C ∆θ
an fuinneamh a theastaíonn chun
staid a athrú
∆ E = ml
∆E = L
r=
friotachas teirmeach
thermal resistivity
l
= lr
k
R=
U-luach (tarchuras teirmeach)
∆E
= AU∆θ
∆t
U=
1
ΣR
thermal conductivity
1
k
R-luach (friotaíocht theirmeach)
U-luach de bhacainn ilchodach
energy needed to change state
∆E
∆θ
= kA
∆t
∆l
seoltacht theirmeach
1
U
=
- 58 -
energy needed to change
temperature
1
U1
R-value (thermal resistance)
U-value (thermal transmittance)
+
1
U2
+ ...
U-value of a composite barrier
Solas agus fuaim
treoluas fuaime
Light and sound
c = fλ
fc
c±u
Doppler effect
1 T
2l µ
fundamental frequency of a
stretched string
iarmhairt Doppler
f ′=
minicíocht bhunúsach sreinge rite
f =
comhéifeacht athraonta
gríl díraonta
fuinneamh fótóin
dlí fótaileictreach Einstein
velocity of a wave
n=
c1
c2
refractive index
nλ = d sin θ
diffraction grating
E = hf
energy of a photon
2
h f = Φ + 12 mvmax
; Φ = hf0
- 59 -
Einstein’s photoelectric law
Optaic gheoiméadrach
Geometric optics
1
foirmle lionsa agus scannáin
f
=
1
u
+
formhéadú
m=
v
u
cumhacht lionsa
P=
1
dhá lionsa thanaí i dteagmháil
le chéile
comhéifeacht athraonta
1
v
f
P = P1 + P2
n=
sin i
1
=
sin r sin C
- 60 -
mirror and lens formula
magnification
power of a lens
two thin lenses in contact
refractive index
Leictreachas
dlí Coulomb
Electricity
F=
q1 q 2
1
4 πε d 2
Coulomb’s law
neart réimse leictrigh
E=
F
q
electric field strength
difríocht poitéinsil
V=
W
q
potential difference
friotaíocht
R=
V
I
resistance
RA
l
resistivity
ρ=
friotachas
friotóirí i sraithcheangal
friotóirí i dtreocheangal
droichead Wheatstone
dlí Joule
R = R1 + R2
1
R
=
1
R1
+
1
R2
resistors in series
resistors in parallel
R1 R3
=
R2 R4
Wheatstone bridge
P∝I2
Joule’s law
- 61 -
P = VI
cumhacht (mheandrach)
fórsa ar sheoltóir sruthiompartha
F = IlB;
l⊥B
fórsa ar cháithnín luchtaithe
F = qvB;
v⊥B
voltas agus sruth ailtéarnach
toilleas
toilleoir plátaí comhthreomhara
an fuinneamh atá stóráilte
i dtoilleoir
dΦ
dt
E=−
flg ionduchtaithe
Vr m s =
V0
I r ms =
2
C=
C=
W=
power (instantaneous)
force on a current-carrying
conductor
force on a charged particle
q
V
ε0 A
d
1
CV 2
2
induced emf
I0
2
alternating voltage and current
capacitance
parallel-plate capacitor
energy stored in capacitor
flosc maighnéadach
Φ = BA
magnetic flux
claochladán
Vi N p
=
Vo N s
transformer
- 62 -
Radaighníomhaíocht
gníomhaíocht
dlí an mheatha radaighníomhaigh
leath-ré
coibhéis mhaise is fuinnimh
Radioactivity
dN
dt
A=−
A = λN
T1 2 =
ln 2
activity
law of radioactive decay
λ
half-life
E = mc2
mass-energy equivalence
- 63 -
Ceimic
Chemistry
teocht chaighdeánach
273.15 K
tríphointe an uisce
273.16 K
brú caighdeánach
standard temperature
triple point of water
5
standard pressure
1.01325 × 10 Pa
toirt mhólarach (ina lítir) ag brú agus
teocht chaighdeánach
molar volume (in litres) at standard
temperature and pressure
22.4
+
+
pH
pH = – log10[H ] = – log10[H3O ]
toradh ianach an uisce
Kw = [H ] [OH ] = [H3O ] [OH ]
ionic product of water
pV = nRT = NkT
universal gas equation
cothromóid uilíoch an gháis
aonad maise (adamhaí)
+
–
+
1 u = 1.660 5402 × 10–27 kg
- 64 -
–
pH
(atomic) mass unit
Siombailí do chainníochtaí fisiceacha
coitianta agus na haonaid
ina dtomhaistear iad
Symbols and units of measurement
of common physical quantities
Braitheann brí siombailí áirithe ar an gcomhthéacs ina
n-úsáidtear iad. In ord aibítre na siombailí atá an tábla.
Tá na litreacha Gréigise chun deiridh.
The meaning of some symbols depends on the context in
which they are used. The table is alphabetically ordered
by symbol. Greek letters are at the end.
Cainníocht
Siombail
Symbol
Aonad SI
SI unit
luasghéarú
a
m s–2
gníomhaíocht
A
Bq
activity
aimplitiúid
A
m
amplitude
achar
A
2
m
area
maisuimhir
A
kg
mass number
mais adamhach choibhneasta
Ar
floscdhlús maighnéadach
B
tiúchan
c
saintoilleadh teasa
luas an tsolais
luas an tsolais in vacuo
c
c
c0
Quantity
acceleration
relative atomic mass
T
magnetic flux density
–3
mol m
J kg–1 K–1
m s–1
m s–1
- 65 -
concentration
specific heat capacity
speed of light
speed of light in vacuo
Siombail
Symbol
Aonad SI
SI unit
toilleas
C
F
uillinn chriticiúil
C
Cainníocht
Quantity
capacitance
critical angle
–1
toilleadh teasa
C
JK
fad slí
d
m
distance
dáileog ionsúite
D
Gy
absorbed dose
lucht leictreonach
e
C
electronic charge
comhéifeacht an chúitimh
e
fuinneamh gníomhachtúcháin
heat capacity
coefficient of restitution
E
J mol
–1
–1
activation energy
neart réimse leictrigh
E
Vm
electric field strength
flg (fórsa leictreaghluaisneach)
E
V
emf (electromotive force)
fuinneamh
E
J
energy
–2
modal Young
E
fuinneamh (cinéiteach)
Ek
J
energy (kinetic)
fuinneamh (poitéinsiúil)
Ep
J
energy (potential)
fad fócasach
f
m
focal length
minicíocht
f
Hz
frequency
minicíocht tairsí
f0
Hz
threshold frequency
Nm
- 66 -
Young’s modulus
Cainníocht
tairiseach Faraday
fórsa
Siombail
Symbol
F
F
Aonad SI
SI unit
C mol–1
N
luasghéarú de bharr
na domhantarraingthe
tairiseach na himtharraingthe
tairiseach Planck
coibhéis dháileogach
g
m s–2
G
h
H
m3 kg–1 s–2
Js
Sv
eantalpacht
H
J mol–1
–1
Quantity
Faraday constant
force
acceleration due to gravity
gravitational constant
Planck constant
dose equivalent
enthalpy
neart réimse mhaighnéadaigh
H
Am
magnetic field strength
sruth leictreach
I
A
electric current
ríog
I
Ns
móimint na táimhe
fuaimdhéine
leibhéal fuaimdhéine
I
impulse
2
moment of inertia
–2
sound intensity
kg m
I
Wm
I.L.
sound intensity level
déine lonrúil
Iν
cd
tairiseach (cineálach)
tairiseach Boltzmann
seoltacht theirmeach
k
k
k
J K–1
W m–1 K–1
- 67 -
luminous intensity
constant (generic)
Boltzmann constant
thermal conductivity
Siombail
Symbol
Aonad SI
SI unit
Quantity
Kw
mol 2 m–6
ionic product of water
fad
l
m
length
móiminteam uilleach
L
Js
angular momentum
teas folaigh
L
J
latent heat
uathionduchtas
L
H
self inductance
formhéadú
m
mais
m
Cainníocht
toradh ianach an uisce
magnification
kg
mass
–3
mólaracht
M
mol m
molarity
móimint fórsa
M
Nm
moment of a force
comhionduchtas
M
H
mutual inductance
mais mhóilíneach choibhneasta
Mr
méid substainte
n
comhéifeacht athraonta
n
refractive index
líon cáithníní
N
number of particles
líon cor
tairiseach Avogadro
neart poil mhaighnéadaigh
N
NA
p
relative molecular mass
mol
–1
mol
Wb
- 68 -
amount of substance
number of turns
Avogadro constant
magnetic pole strength
Cainníocht
Siombail
Symbol
Aonad SI
SI unit
móiminteam
p
kg m s–1
p, P
Pa
pressure
cumhacht
P
W
power
lucht
q
C
charge
fuinneamh (teas)
Q
J
brú
Quantity
momentum
energy (heat)
–1
friotachas teirmeach
r
frithghníomhú normalach
R
N
normal reaction
friotachas
R
Ω
resistance
r, R
m
radius
R-luach (friotaíocht theirmeach)
tairiseach uilíoch gáis
díláithriú, fad
R
R
s
K m2 W–1
J K–1 mol–1
m
am
t
s
teocht Celsius
t, θ
°C
am tréimhsiúil
T
s
periodic time
teocht
T
K
temperature
teannas
T
N
tension
ga
KmW
- 69 -
thermal resistivity
R-value (thermal resistance)
universal gas constant
displacement, distance
time
Celsius temperature
Cainníocht
torc
leathré
U-luach (tarchuras teirmeach)
luas, treoluas
Siombail
Symbol
Aonad SI
SI unit
T
Nm
T1 2
s
U
–2
torque
half-life
Wm K
u
Quantity
–1
U-value (thermal transmittance)
ms
–1
speed, velocity
–1
speed, velocity
luas, treoluas
v
ms
difríocht poitéinsil (voltas)
V
V
potential difference (voltage)
toirt
V
3
m
volume
fuinneamh (leictreach)
W
J
energy (electrical)
meáchan
W
N
obair
W
J
uimhir adamhach
Z
athrú teochta
∆θ
weight
work
atomic number
K
change in temperature
–1
permittivity
permittivity of free space
ceadaíocht
ε
Fm
ceadaíocht an tsaorspáis
ε0
F m–1
straidhn
ε
uillinn
θ
strain
rad
- 70 -
angle
Siombail
Symbol
Aonad SI
SI unit
teocht Celsius
θ
°C
Celsius temperature
tonnfhad
λ
m
wavelength
comhéifeacht na frithchuimilte
tréscaoilteacht
tréscaoilteacht an tsaorspáis
µ
µ
µ0
H m–1
coefficient of friction
permeability
permeability of free space
dlús
ρ
kg m–3
density
friotachas
ρ
Ωm
strus
σ
Pa
stress
flosc maighnéadach
Φ
Wb
magnetic flux
feidhm oibre
Φ
J
work function
Cainníocht
–1
Hm
treoluas uilleach
ω
rad s
uillinn sholadach
Ω
sr
- 71 -
–1
Quantity
resistivity
angular velocity
solid angle
Siombailí ciorcaid leictrigh
Electrical circuit symbols
Lasca
Switches
sá-lasc chun ceangail
sá-lasc chun gearrtha
lasc gnáthoscailte
(lasc aon phoil aon
bhealaigh) (SPST)
push-to-make switch
push-to-break switch
normally open switch
(single-pole single-throw
switch) (SPST)
normally closed switch
(SPST)
lasc dhá bhealach
(lasc aon phoil
dhébhealaigh) (SPDT)
lasc phoil dhúbailte aon
bhealaigh (DPST)
lasc phoil dhúbailte
dhébhealaigh (DPDT)
athsheachadán
two-way switch
(single-pole doublethrow switch) (SPDT)
double-pole single-throw
switch (DPST)
double-pole double-throw
switch (DPDT)
relay
- 72 -
lasc gnáthdhúnta
(SPST)
Seoltóirí
Conductors
cumar seoltóirí
seoltóirí ag trasnú a chéile
gan cheangal
junction of conductors
conductors crossing with
no connection
Soláthar cumhachta
Power supply
cill
ceallra
soláthar s.d.
soláthar s.a.
cell
battery
d.c. supply
a.c. supply
cill fhótavoltach
claochladán
fiús
talmhú
photovoltaic cell
transformer
fuse
earth
- 73 -
Friotóirí
Resistors
friotóir fosaithe
friotóir inathraithe
(réastat)
friotóir inathraithe
réamhshocraithe
roinnteoir poitéinsil
fixed resistor
variable resistor
(rheostat)
preset variable resistor
potential divider
teirmeastar
friotóir solas-spleách
thermistor
light-dependent resistor
Toilleoirí
Capacitors
toilleoir
toilleoir leictrealaíoch
(toilleoir polaraithe)
toilleoir inathraithe
toilleoir inathraithe
réamhshocraithe
capacitor
electrolytic capacitor
(polarised capacitor)
variable capacitor
preset variable capacitor
- 74 -
Dé-óidí
Diodes
dé-óid
dé-óid Zener
fótaidhé-óid
dé-óid astaithe solais
(LED)
diode
Zener diode
photodiode
light-emitting diode
(LED)
Méadair
voltmhéadar
Meters
galbhánaiméadar
aimpmhéadar
óm-mhéadar
Ω
voltmeter
galvanometer
ammeter
ascalascóp
oscilloscope
- 75 -
ohmmeter
Trasraitheoirí agus aimpliú
Transistors and amplification
trasraitheoir cumair npn
trasraitheoir tionchar
réimse n-chainéil (JFET)
fótathrasraitheoir
aimplitheoir
npn-junction transistor
n-channel field-effect
transistor (JFET)
phototransistor
amplifier
Fuaim
Audio
micreafón
cluasán
callaire
cloigín
microphone
earphone
loudspeaker
bell
dordánaí
trasduchtóir písileictreach
aeróg
buzzer
piezoelectric transducer
aerial (antenna)
- 76 -
Lampaí
Lamps
lampa filiméid
lampa comhartha
lampa neoin
filament lamp
signal lamp
neon lamp
Feistí eile
Other devices
mótar
téitheoir
ionduchtóir
ionduchtóir le croíleacán
fearómaighnéadach
heater
inductor
inductor with
ferromagnetic core
M
motor
- 77 -
Geataí loighce
Logic gates
≥1
&
=1
&
OR
AND
NOT
(inbhéartóir / inverter)
NAND
≥1
NOR
- 78 -
Na dúile
The elements
Tábla peiriadach na ndúl
Periodic table of the elements
1
18
1
2
H
He
1.008
2
13
14
15
16
17
3
4
5
6
7
8
9
10
Li
Be
B
C
N
O
F
Ne
6.941
9.012
10.81
12.01
14.01
16.00
19.00
20.18
11
12
13
14
15
16
17
18
4.003
Na
Mg
Al
Si
P
S
Cl
Ar
22.99
24.31
3
4
5
6
7
8
9
10
11
12
26.98
28.09
30.97
32.07
35.45
39.95
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
39.10
40.08
44.96
47.87
50.94
52.00
54.94
55.85
58.93
58.69
63.55
65.41
69.72
72.64
74.92
78.96
79.90
83.80
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
85.47
87.62
88.91
91.22
92.91
95.94
(97.91)
101.1
102.9
106.4
107.9
112.4
114.8
118.7
121.8
127.6
126.9
131.3
55
56
57
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
132.9
137.3
138.9
178.5
180.9
183.8
186.2
190.2
192.2
195.1
197.0
200.6
204.4
207.2
209.0
(209.0)
(210.0)
(222.0)
87
88
89
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
Fr
Ra
Ac
Rf
Db
Sg
Bh
Hs
Mt
Ds
Rg
(223.0)
(226.0)
(227.0)
(261.1)
(262.1)
(266.1)
(264.1)
(277.0)
(268.1)
(271.0)
(272.2)
* Níor braitheadh an dúil seo go fóill (2009).
Ar lch 82 atá an tSraith Lantanóideach agus an tSraith Achtanóideach.
Cuireann na lúibíní in iúl nach bhfuil iseatóp cobhsaí ag an dúil.
- 79 -
Uub Uut Uuq Uup Uuh Uus* Uuo
(285.0)
(284)
(289.0)
(288)
(289.0)
(293.0)
* This element has not yet been detected (2009).
See page 82 for the Lanthanoid and the Actinoid Series.
Brackets indicate that the element has no stable isotope.
Fuinneamh céadianúcháin na ndúl
(ina kJ mol–1)
First ionisation energies of the elements
(in kJ mol–1)
1
18
1
2
H
1312
He
2
13
14
15
16
17
2372
3
4
5
6
7
8
9
10
Li
Be
B
C
N
O
F
Ne
520
900
801
1086
1402
1314
1681
2081
11
12
13
14
15
16
17
18
Na
Mg
Al
Si
P
S
Cl
Ar
496
738
3
4
5
6
7
8
9
10
11
12
578
789
1012
1000
1251
1521
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
419
590
631
658
650
653
717
759
758
737
746
906
579
762
947
941
1140
1351
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
403
550
616
660
665
685
702
711
720
805
731
868
558
709
834
869
1008
1170
55
56
57
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
376
503
538
680
761
770
760
840
880
870
890
1007
589
716
703
812
890±40
1037
112
113
114
115
116
117
118
87
88
89
104
105
106
107
108
109
110
111
Fr
Ra
Ac
Rf
Db
Sg
Bh
Hs
Mt
Ds
Rg
380
509
499
580
––
––
––
––
––
––
––
Ar lch 82 atá an tSraith Lantanóideach agus an tSraith Achtanóideach.
- 80 -
Uub Uut Uuq Uup Uuh Uus* Uuo
––
––
––
––
––
––
See page 82 for the Lanthanoid and the Actinoid Series.
Luachanna leictridhiúltachta na ndúl
(Ag baint úsáid as scála Pauling)
Electronegativity values of the elements
(Using the Pauling scale)
1
18
1
2
H
He
2.20
2
13
14
15
16
17
3
4
5
6
7
8
9
10
Li
Be
B
C
N
O
F
Ne
0.98
1.57
2.04
2.55
3.04
3.44
3.98
––
11
12
13
14
15
16
17
18
Na
Mg
Al
Si
P
S
Cl
Ar
0.93
1.31
3
4
5
6
7
8
9
10
11
12
1.61
1.90
2.19
2.58
3.16
––
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
––
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Kr
0.82
1.00
1.36
1.54
1.63
1.66
1.55
1.83
1.88
1.91
1.90
1.65
1.81
2.01
2.18
2.55
2.96
––
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
0.82
0.95
1.22
1.33
1.60
2.16
2.10
2.20
2.28
2.20
1.93
1.69
1.78
1.96
2.05
2.10
2.66
2.60
55
56
57
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
Rn
Cs
Ba
La
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
0.79
0.89
1.10
1.30
1.50
1.70
1.90
2.20
2.20
2.20
2.40
1.90
1.80
1.80
1.90
2.00
2.20
––
87
88
89
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
Fr
Ra
Ac
Rf
Db
Sg
Bh
Hs
Mt
Ds
Rg
0.70
0.90
1.10
––
––
––
––
––
––
––
––
Ar lch 82 atá an tSraith Lantanóideach agus an tSraith Achtanóideach.
- 81 -
Uub Uut Uuq Uup Uuh Uus* Uuo
––
––
––
––
––
––
See page 82 for the Lanthanoid and the Actinoid Series.
Tábla peiriadach na ndúl
An tSraith
Lantanóideach
Lanthanoid Series
An tSraith
Achtanóideach
Actinoid Series
58
Periodic table of the elements
59
60
61
62
63
64
65
68
69
70
71
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
140.9
144.2
(144.9)
150.4
152.0
157.3
158.9
162.5
164.9
167.3
168.9
173.0
175.0
90
91
92
93
94
95
96
97
98
99
100
101
102
103
No
Lr
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
232.0
231.0
238.0
(237.0)
(244.1)
(243.1)
(247.1)
(247.1)
(251.1)
(252.1)
(257.1)
(258.1)
(259.1) (262.1)
Brackets indicate that the element has no stable isotope.
Fuinneamh céadianúcháin na ndúl
(ina kJ mol–1)
First ionisation energies of the elements
(in kJ mol–1)
58
59
60
61
62
63
64
65
66
67
68
69
70
71
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
534
527
533
540
545
547
593
566
573
581
589
597
603
524
90
91
92
93
94
95
96
97
98
99
100
101
102
103
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
587
568
598
605
581
576
581
601
608
619
627
635
642
470
Luachanna leictridhiúltachta na ndúl
(Ag baint úsáid as scála Pauling)
An tSraith
Lantanóideach
Lanthanoid Series
An tSraith
Achtanóideach
Actinoid Series
67
140.1
Cuireann na lúibíní in iúl nach bhfuil iseatóp cobhsaí ag an dúil.
An tSraith
Lantanóideach
Lanthanoid Series
An tSraith
Achtanóideach
Actinoid Series
66
Electronegativity values of the elements
(Using the Pauling scale)
58
59
60
61
62
63
64
65
66
67
68
69
70
71
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
1.12
1.13
1.14
––
1.17
––
1.20
––
1.22
1.23
1.24
1.25
––
1.00
90
91
92
93
94
95
96
97
98
99
100
101
102
103
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
1.30
1.50
1.70
1.30
1.30
1.30
1.30
1.30
1.30
1.30
1.30
1.30
1.30
1.30
- 82 -
Tábla na núiclídí
Table of nuclides
Liosta atá sa tábla de mhaiseanna na núiclídí cobhsaí agus
de mhaiseanna na n-iseatóp is fadsaolaí de na núiclídí
éagobhsaí. Tugtar céatadán líonmhaireachta nádúrtha
na núiclídí cobhsaí agus leathré na n-iseatóp is fadsaolaí
de na núiclídí éagobhsaí. Tugtar sonraí breise i gcomhair
an úráiniam.
Z
1
2
3
4
5
6
7
siombail
symbol
1
H
2
H
3
H
3
He
4
He
6
Li
7
Li
9
Be
10
B
11
B
12
C
13
C
14
C
14
N
mais adaimh
mass of atom
(u)
1.007 825
2.014 102
3.016 049
3.016 029
4.002 603
6.015 123
7.016 005
9.012 182
10.012 937
11.009 305
12.000 000
13.003 355
14.003 242
14.003 074
líonmhaireacht
abundance
(%)
99.9885
0.0115
–
0.000134
99.999866
7.59
92.41
100
19.9
80.1
98.93
1.07
–
99.636
The table lists the mass of the stable nuclides and that of
the longest-lived isotope of the unstable nuclides. The
percentage natural abundance is given for the stable
nuclides and the half-life is given for the longest-lived
isotope of the unstable nuclides. Additional information is
given for uranium.
leathré
half-life
Z
siombail
symbol
15
8
12.33 y
9
10
11
12
5730 y
13
14
- 83 -
N
O
17
O
18
O
19
F
20
Ne
21
Ne
22
Ne
23
Na
24
Mg
25
Mg
26
Mg
27
Al
28
Si
16
mais adaimh
mass of atom
(u)
15.000 109
15.994 915
16.999 132
17.999 161
18.998 403
19.992 440
20.993 847
21.991 385
22.989 769
23.985 042
24.985 837
25.982 593
26.981 538
27.976 927
líonmhaireacht
abundance
(%)
0.364
99.757
0.038
0.205
100
90.48
0.27
9.25
100
78.99
10.00
11.01
100
92.223
leathré
half-life
Z
siombail
symbol
29
Si
Si
31
P
32
S
33
S
34
S
36
S
35
Cl
37
Cl
36
Ar
38
Ar
40
Ar
39
K
40
K
41
K
40
Ca
42
Ca
43
Ca
44
Ca
46
Ca
48
Ca
30
15
16
17
18
19
20
mais adaimh
mass of atom
(u)
28.976 495
29.973 770
30.973 762
31.972 071
32.971 458
33.967 867
35.967 081
34.968 853
36.965 903
35.967 545
37.962 732
39.962 383
38.963 707
39.963 999
40.961 826
39.962 591
41.958 618
42.958 767
43.955 482
45.953 693
47.952 534
líonmhaireacht
abundance
(%)
leathré
half-life
Z
4.685
3.092
100
94.99
0.75
4.25
0.01
75.76
24.24
0.3365
0.0632
99.6003
93.2581
0.0117
6.7302
96.941
0.647
0.135
2.086
0.004
0.187
21
22
23
24
25
26
27
28
- 84 -
siombail
symbol
45
Sc
Ti
47
Ti
48
Ti
49
Ti
50
Ti
50
V
51
V
50
Cr
52
Cr
53
Cr
54
Cr
55
Mn
54
Fe
56
Fe
57
Fe
58
Fe
59
Co
58
Ni
60
Ni
61
Ni
46
mais adaimh
mass of atom
(u)
44.955 912
45.952 632
46.951 763
47.947 946
48.947 870
49.944 791
49.947 159
50.943 960
49.946 044
51.940 508
52.940 649
53.938 880
54.938 045
53.939 611
55.934 938
56.935 394
57.933 276
58.933 195
57.935 343
59.930 786
60.931 056
líonmhaireacht
abundance
(%)
100
8.25
7.44
73.72
5.41
5.18
0.250
99.750
4.345
83.789
9.501
2.365
100
5.845
91.754
2.119
0.282
100
68.0769
26.2231
1.1399
leathré
half-life
Z
siombail
symbol
62
Ni
Ni
63
Cu
65
Cu
64
Zn
66
Zn
67
Zn
68
Zn
70
Zn
69
Ga
71
Ga
70
Ge
72
Ge
73
Ge
74
Ge
76
Ge
75
As
74
Se
76
Se
77
Se
78
Se
64
29
30
31
32
33
34
mais adaimh
mass of atom
(u)
61.928 345
63.927 966
62.929 598
64.927 790
63.929 142
65.926 033
66.927 127
67.924 844
69.925 319
68.925 574
70.924 701
69.924 247
71.922 076
72.923 459
73.921 178
75.921 403
74.921 597
73.922 476
75.919 214
76.919 914
77.917 309
líonmhaireacht
abundance
(%)
leathré
half-life
Z
siombail
symbol
80
3.6345
0.9256
69.15
30.85
48.268
27.975
4.102
19.024
0.631
60.108
39.892
20.38
27.31
7.76
36.72
7.83
100
0.89
9.37
7.63
23.77
Se
Se
79
Br
81
Br
78
Kr
80
Kr
82
Kr
83
Kr
84
Kr
86
Kr
85
Rb
87
Rb
84
Sr
86
Sr
87
Sr
88
Sr
89
Y
90
Zr
91
Zr
92
Zr
94
Zr
82
35
36
37
38
39
40
- 85 -
mais adaimh
mass of atom
(u)
79.916 521
81.916 700
78.918 337
80.916 291
77.920 365
79.916 379
81.913 484
82.914 136
83.911 507
85.910 611
84.911 790
86.909 181
83.913 425
85.909 260
86.908 877
87.905 612
88.905 848
89.904 704
90.905 645
91.905 041
93.906 315
líonmhaireacht
abundance
(%)
49.61
8.73
50.69
49.31
0.355
2.286
11.593
11.500
56.987
17.279
72.17
27.83
0.56
9.86
7.00
82.58
100
51.45
11.22
17.15
17.38
leathré
half-life
Z
siombail
symbol
96
41
42
43
44
45
46
Zr
Nb
92
Mo
94
Mo
95
Mo
96
Mo
97
Mo
98
Mo
100
Mo
98
Tc
96
Ru
98
Ru
99
Ru
100
Ru
101
Ru
102
Ru
104
Ru
103
Rh
102
Pd
104
Pd
105
Pd
93
mais adaimh
mass of atom
(u)
95.908 273
92.906 378
91.906 811
93.905 088
94.905 842
95.904 680
96.906 020
97.905 408
99.907 477
97.907 216
95.907 598
97.905 287
98.905 939
99.904 220
100.905 582
101.904 350
103.905 433
102.905 504
101.905 609
103.904 036
104.905 085
líonmhaireacht
abundance
(%)
2.80
100
14.77
9.23
15.90
16.68
9.56
24.19
9.67
–
5.54
1.87
12.76
12.60
17.06
31.55
18.62
100
1.02
11.14
22.33
leathré
half-life
Z
siombail
symbol
106
Pd
Pd
110
Pd
107
Ag
109
Ag
106
Cd
108
Cd
110
Cd
111
Cd
112
Cd
113
Cd
114
Cd
116
Cd
113
In
115
In
112
Sn
114
Sn
115
Sn
116
Sn
117
Sn
118
Sn
108
47
48
4.2 × 106 y
49
50
- 86 -
mais adaimh
mass of atom
(u)
105.903 486
107.903 892
109.905 153
106.905 097
108.904 752
105.906 459
107.904 184
109.903 002
110.904 178
111.902 758
112.904 402
113.903 359
115.904 756
112.904 058
114.903 878
111.904 819
113.902 780
114.903 342
115.901 741
116.902 952
117.901 603
líonmhaireacht
abundance
(%)
27.33
26.46
11.72
51.839
48.161
1.25
0.89
12.49
12.80
24.13
12.22
28.73
7.49
4.29
95.71
0.97
0.66
0.34
14.54
7.68
24.22
leathré
half-life
Z
siombail
symbol
119
Sn
Sn
122
Sn
124
Sn
121
Sb
123
Sb
120
Te
122
Te
123
Te
124
Te
125
Te
126
Te
128
Te
130
Te
127
I
124
Xe
126
Xe
128
Xe
129
Xe
130
Xe
131
Xe
120
51
52
53
54
mais adaimh
mass of atom
(u)
118.903 308
119.902 195
121.903 440
123.905 274
120.903 816
122.904 214
119.904 020
121.903 044
122.904 270
123.902 818
124.904 431
125.903 312
127.904 463
129.906 224
126.904 473
123.905 893
125.904 274
127.903 531
128.904 779
129.903 508
130.905 082
líonmhaireacht
abundance
(%)
leathré
half-life
Z
siombail
symbol
132
8.59
32.58
4.63
5.79
57.21
42.79
0.09
2.55
0.89
4.74
7.07
18.84
31.74
34.08
100
0.0952
0.0890
1.9102
26.4006
4.0710
21.2324
Xe
Xe
136
Xe
133
Cs
130
Ba
132
Ba
134
Ba
135
Ba
136
Ba
137
Ba
138
Ba
138
La
139
La
136
Ce
138
Ce
140
Ce
142
Ce
141
Pr
142
Nd
143
Nd
144
Nd
134
55
56
57
58
59
60
- 87 -
mais adaimh
mass of atom
(u)
131.904 154
133.905 395
135.907 220
132.905 452
129.906 321
131.905 061
133.904 508
134.905 687
135.904 576
136.905 827
137.905 247
137.907 112
138.906 353
135.907 172
137.905 991
139.905 439
141.909 244
140.907 643
141.907 723
142.909 814
143.910 088
líonmhaireacht
abundance
(%)
26.9086
10.4357
8.8573
100
0.106
0.101
2.417
6.592
7.854
11.232
71.698
0.090
99.910
0.185
0.251
88.450
11.114
100
27.2
12.2
23.8
leathré
half-life
Z
siombail
symbol
145
Nd
Nd
148
Nd
150
Nd
145
Pm
144
Sm
147
Sm
148
Sm
149
Sm
150
Sm
152
Sm
154
Sm
151
Eu
153
Eu
152
Gd
154
Gd
155
Gd
156
Gd
157
Gd
158
Gd
160
Gd
146
61
62
63
64
mais adaimh
mass of atom
(u)
144.912 574
145.913 117
147.916 893
149.920 891
144.912 744
143.911 999
146.914 898
147.914 823
148.917 185
149.917 276
151.919 732
153.922 209
150.919 850
152.921 230
151.919 791
153.920 866
154.922 622
155.922 123
156.923 960
157.924 104
159.927 054
líonmhaireacht
abundance
(%)
8.3
17.2
5.7
5.6
–
3.07
14.99
11.24
13.82
7.38
26.75
22.75
47.81
52.19
0.20
2.18
14.80
20.47
15.65
24.84
21.86
leathré
half-life
Z
65
66
17.7 y
67
68
69
70
- 88 -
siombail
symbol
159
Tb
Dy
158
Dy
160
Dy
161
Dy
162
Dy
163
Dy
164
Dy
165
Ho
162
Er
164
Er
166
Er
167
Er
168
Er
170
Er
169
Tm
168
Yb
170
Yb
171
Yb
172
Yb
173
Yb
156
mais adaimh
mass of atom
(u)
158.925 347
155.924 283
157.924 409
159.925 198
160.926 933
161.926 798
162.928 731
163.929 175
164.930 322
161.928 778
163.929 200
165.930 293
166.932 048
167.932 370
169.935 464
168.934 213
167.933 897
169.934 762
170.936 326
171.936 382
172.938 211
líonmhaireacht
abundance
(%)
100
0.056
0.095
2.29
18.889
25.475
24.896
28.260
100
0.139
1.601
33.503
22.869
26.978
14.910
100
0.13
3.04
14.28
21.83
16.13
leathré
half-life
Z
siombail
symbol
174
Yb
Yb
175
Lu
176
Lu
174
Hf
176
Hf
177
Hf
178
Hf
179
Hf
180
Hf
180
Ta
181
Ta
180
W
182
W
183
W
184
W
186
W
185
Re
187
Re
184
Os
186
Os
176
71
72
73
74
75
76
mais adaimh
mass of atom
(u)
173.938 862
175.942 572
174.940 772
175.942 686
173.940 046
175.941 409
176.943 221
177.943 699
178.945 816
179.946 550
179.947 465
180.947 996
179.946 704
181.948 204
182.950 223
183.950 931
185.954 364
184.952 955
186.955 753
183.952 489
185.953 838
líonmhaireacht
abundance
(%)
leathré
half-life
Z
siombail
symbol
187
31.83
12.76
97.41
2.59
0.16
5.26
18.60
27.28
13.62
35.08
0.012
99.988
0.12
26.50
14.31
30.64
28.43
37.40
62.60
0.02
1.59
Os
Os
189
Os
190
Os
192
Os
191
Ir
193
Ir
190
Pt
192
Pt
194
Pt
195
Pt
196
Pt
198
Pt
197
Au
196
Hg
198
Hg
199
Hg
200
Hg
201
Hg
202
Hg
204
Hg
188
77
78
79
80
- 89 -
mais adaimh
mass of atom
(u)
186.955 751
187.955 838
188.958 148
189.958 447
191.961 481
190.960 594
192.962 926
189.959 932
191.961 038
193.962 680
194.964 791
195.964 952
197.967 893
196.966 569
195.965 833
197.966 769
198.968 280
199.968 326
200.970 302
201.970 643
203.973 494
líonmhaireacht
abundance
(%)
1.96
13.24
16.15
26.26
40.78
37.3
62.7
0.014
0.782
32.967
33.832
25.242
7.163
100
0.15
9.97
16.87
23.10
13.18
29.86
6.87
leathré
half-life
Z
81
siombail
symbol
203
Tl
Tl
204
Pb
206
Pb
207
Pb
208
Pb
209
Bi
209
Po
210
At
222
Rn
223
Fr
226
Ra
227
Ac
232
Th
231
Pa
234
U
235
U
238
U
237
Np
244
Pu
243
Am
205
82
83
84
85
86
87
88
89
90
91
92
93
94
95
mais adaimh
mass of atom
(u)
202.972 344
204.974 428
203.973 044
205.974 465
206.975 897
207.976 652
208.980 379
208.982 430
209.987 150
222.017 578
223.019 736
226.025 410
227.027 752
232.038 055
231.035 884
234.040 952
235.043 930
238.050 788
237.048 167
244.067 900
243.061 381
líonmhaireacht
abundance
(%)
29.52
70.48
1.4
24.1
22.1
52.4
100
–
–
–
–
–
–
–
–
0.0054
0.7204
99.2742
–
–
–
leathré
half-life
Z
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
118
103 y
8.1 h
3.824 d
22.0 min
1602 y
21.77 y
1.4 × 1010 y
3.28× 104 y
2.46 × 106 y
7.04 × 108 y
4.47 × 109 y
2.14 × 106 y
8.08 × 107 y
7.37× 103 y
- 90 -
siombail
symbol
247
Cm
Bk
251
Cf
252
Es
257
Fm
258
Md
259
No
262
Lr
263
Rf
262
Db
266
Sg
264
Bh
269
Hs
268
Mt
273
Ds
272
Rg
285
Uub
284
Uut
289
Uuq
288
Uup
293
Uuh
294
Uuo
247
mais adaimh
mass of atom
(u)
líonmhaireacht
abundance
(%)
leathré
half-life
247.070 354
247.070 310
251.079 587
252.082 980
257.095 110
258.098 431
259.101 024
262.1096
263.1126
262.1141
266.1221
264.1246
269.1341
268.1387
272.1489
272.1536
285.174
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
1.56 × 107 y
1.38 × 103 y
898 y
1.29 y
100.5 d
51.5 d
57 min
3.6 h
10.0 min
0.5 min
~ 21 s
1.0 s
~ 14 s
~ 42 ms
118 ms
~ 2 ms
~34 s
~ 0.49 s
~ 2.7 s
~ 87.5 ms
~ 0.05 s
~ 2.0 ms
284.178
289.187
288.192
(293)
(294)
Dúile, sórtáilte de réir na siombailí
Dúil
achtainiam
airgead
alúmanam
aimeiriciam
argón
arsanaic
astaitín
ór
bórón
bairiam
beirilliam
bóiriam
biosmat
beircéiliam
bróimín
carbón
cailciam
caidmiam
ceiriam
calafoirniam
clóirín
Siombail
Symbol
Ac
Ag
Al
Am
Ar
As
At
Au
B
Ba
Be
Bh
Bi
Bk
Br
C
Ca
Cd
Ce
Cf
Cl
Z
Element
89
47
13
95
18
33
85
79
5
56
4
107
83
97
35
6
20
48
58
98
17
actinium
silver
aluminium
americium
argon
arsenic
astatine
gold
boron
barium
beryllium
bohrium
bismuth
berkelium
bromine
carbon
calcium
cadmium
cerium
californium
chlorine
Elements, sorted by symbol
Dúil
ciúiriam
cóbalt
cróimiam
caeisiam
copar
deoitéiriam
dúibniam
darmstaidiam
diospróisiam
eirbiam
éinstéiniam
eoraipiam
fluairín
iarann
feirmiam
frainciam
gailliam
gadailiniam
gearmáiniam
hidrigin
héiliam
- 91 -
Siombail
Symbol
Cm
Co
Cr
Cs
Cu
D
Db
Ds
Dy
Er
Es
Eu
F
Fe
Fm
Fr
Ga
Gd
Ge
H
He
Z
Element
96
27
24
55
29
1
105
110
66
68
99
63
9
26
100
87
31
64
32
1
2
curium
cobalt
chromium
caesium
copper
deuterium
dubnium
darmstadtium
dysprosium
erbium
einsteinium
europium
fluorine
iron
fermium
francium
gallium
gadolinium
germanium
hydrogen
helium
Dúil
haifniam
mearcair
hoilmiam
haisiam
iaidín
indiam
iridiam
potaisiam
crioptón
lantanam
litiam
láirinciam
lúitéitiam
meindiléiviam
maignéisiam
mangainéis
molaibdéineam
meitniriam
nítrigin
sóidiam
niaibiam
neoidimiam
neon
Siombail
Symbol
Hf
Hg
Ho
Hs
I
In
Ir
K
Kr
La
Li
Lr
Lu
Md
Mg
Mn
Mo
Mt
N
Na
Nb
Nd
Ne
Z
Element
72
80
67
108
53
49
77
19
36
57
3
103
71
101
12
25
42
109
7
11
41
60
10
hafnium
mercury
holmium
hassium
iodine
indium
iridium
potassium
krypton
lanthanum
lithium
lawrencium
lutetium
mendelevium
magnesium
manganese
molybdenum
meitnerium
nitrogen
sodium
niobium
neodymium
neon
Dúil
nicil
nóbailiam
neiptiúiniam
ocsaigin
oismiam
fosfair
prótachtainiam
luaidhe
pallaidiam
próiméitiam
polóiniam
praiséidimiam
platanam
plútóiniam
raidiam
rubaidiam
réiniam
rutarfoirdiam
rointginiam
róidiam
radón
ruitéiniam
sulfar
- 92 -
Siombail
Symbol
Ni
No
Np
O
Os
P
Pa
Pb
Pd
Pm
Po
Pr
Pt
Pu
Ra
Rb
Re
Rf
Rg
Rh
Rn
Ru
S
Z
Element
28
102
93
8
76
15
91
82
46
61
84
59
78
94
88
37
75
104
111
45
86
44
16
nickel
nobelium
neptunium
oxygen
osmium
phosphorus
protactinium
lead
palladium
promethium
polonium
praseodymium
platinum
plutonium
radium
rubidium
rhenium
rutherfordium
roentgenium
rhodium
radon
ruthenium
sulfur
Dúil
antamón
scaindiam
seiléiniam
seaboirgiam
sileacan
samairiam
stán
strointiam
tritiam
tantalam
teirbiam
teicnéitiam
teallúiriam
tóiriam
tíotáiniam
tailliam
túiliam
úráiniam
únúinbiam
únúinheicsiam
únúnoichtiam
únúinpeintiam
únúncuaidiam
Siombail
Symbol
Sb
Sc
Se
Sg
Si
Sm
Sn
Sr
T
Ta
Tb
Tc
Te
Th
Ti
Tl
Tm
U
Uub
Uuh
Uuo
Uup
Uuq
Z
Element
51
21
34
106
14
62
50
38
1
73
65
43
52
90
22
81
69
92
112
116
118
115
114
antimony
scandium
selenium
seaborgium
silicon
samarium
tin
strontium
tritium
tantalum
terbium
technetium
tellurium
thorium
titanium
thallium
thulium
uranium
ununbium
ununhexium
ununoctium
ununpentium
ununquadium
Dúil
únúinseiptiam
únúintriam
vanaidiam
tungstan
xeanón
itriam
itéirbiam
sinc
siorcóiniam
- 93 -
Siombail
Symbol
Uus
Uut
V
W
Xe
Y
Yb
Zn
Zr
Z
Element
117
113
23
74
54
39
70
30
40
ununseptium
ununtrium
vanadium
tungsten
xenon
yttrium
ytterbium
zinc
zirconium