Physics Data Booklet
Standard Grade and Access 3
to Advanced Higher
For use in National Qualification Courses
leading to the 2008 examinations and beyond.
Published date: February 2008
Publication code: BB2099
ISBN: 978 1 85969 697 2
Published by the Scottish Qualifications Authority
The Optima Building, 58 Robertson Street, Glasgow G2 8DQ
Ironmills Road, Dalkeith, Midlothian EH22 1LE
www.sqa.org.uk
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Contents
Introduction ....................................................................................................................1
Relationships for Access 3 and/or Intermediate 1 ..........................................................2
Relationships for Standard Grade and/or Intermediate 2 ...............................................3
Relationships for Higher ................................................................................................4
Relationships for Advanced Higher ...............................................................................6
Additional relationships .................................................................................................8
Electron arrangements of elements ................................................................................9
Introduction
This data booklet is intended for use by candidates in examinations in Physics at Standard Grade,
Intermediate 1, Intermediate 2, Higher and Advanced Higher levels from the 2008 examination diet.
It is recommended that candidates become familiar with the contents of the data booklet through
use in undertaking Units of these Courses, including Physics Units at Access 3.
The range of data contained in the booklet has been limited to that syllabus content which may be
assessed through written examination papers. This data should be supplemented by other resource
material as necessary during the course, eg by using data sheets. However, should any additional
information (or data not included in this booklet) be required in an examination, such information
will be included in the examination paper.
Additional relationships, which candidates may find useful, are contained on page 8. A periodic
table of elements is included on page 9.
From the variety of data offered in this booklet, candidates will be expected to demonstrate the
ability to select an appropriate:
♦ formula
♦ relationship
♦ element or data pertaining to an element
1
Relationships for Access 3 and/or Intermediate 1
resistance =
current =
speed =
voltage
current
power
voltage
distance
time
voltage gain =
output voltage
input voltage
weight = 10 × mass
average speed =
distance
time
2
Relationships for Standard Grade and/or Intermediate 2
d = vt
RT = R1 + R2 + ...
s = vt
1
1
1
= +
+ ...
RT R1 R2
a=
Δv
t
a=
v−u
t
⎛ R2 ⎞
V2 = ⎜
⎟ Vs
⎝ R1 + R2 ⎠
W = mg
V1 R1
=
V2 R2
F = ma
P = IV
p = mv
P = I 2R
Ew = Fd
P=
V2
R
Ep = mgh
ns Vs I p
=
=
n p Vp I s
Ek = 12 mv 2
P=
E
t
percentage efficiency =
useful Eo
× 100
Ei
percentage efficiency =
useful Po
× 100
Pi
Vgain =
Vo
Vi
Pgain =
Po
Pi
v = fλ
Eh = cmΔT
P=
1
f
A=
N
t
D=
E
m
Eh = ml
Q = It
V = IR
H = Dw R
3
Relationships for Higher
a=
Δv
t
R1 R3
=
R2 R4
v = u + at
V = IR
P = IV = I 2 R =
s = ut + 12 at 2
Vpeak = 2Vrms
v2 = u2 + 2as
1
I peak = 2 Irms
s = 2 (u + v)t
F = ma
C=
Ew = Fd
Ek = 12 mv2
1
2
Q2
C
Rf
Vo
=−
V1
R1
E
t
Vo = (V2 − V1 )
p = mv
Ft = mv – mu
T=
m
ρ=
V
P=
Q
V
E = 12 QV = 12 CV 2 =
Ep = mgh
P=
V2
R
Rf
R1
1
f
v = fλ
F
A
path difference = nλ
path difference = (n + 12 )λ
P = ρ gh
d sinθ = nλ
PV
= constant
T
n=
W = QV
sin θ1
sin θ 2
sin θ1 λ1 v1
=
=
sin θ 2 λ2 v2
E = V + Ir
Σ E = Σ IR
RT = R1 + R2 + ...
sin θ c =
1
1
1
=
+
+ ...
RT R1 R2
I=
4
k
d2
1
n
Relationships for Higher
E = hf
I = Nhf
I=
P
A
Ek = hf – hf0
W2 – W1 = hf
E = mc2
A=
N
t
D=
E
m
H = Dw R
H
H =
t
random uncertainty =
max. value − min. value
number of values
5
Relationships for Advanced Higher
a=
L = Iω
dv d 2 s
=
dt dt 2
Erot = 12 Iω2
v = u + at
F=
Gm1 m2
r2
s = ut + 12 at 2
v = u + 2as
2
2
mo
m=
1−
v2
c2
V =−
Gm
r
v=
2Gm
r
ω = 2π f
E = mc2
d2 y
= −ω 2 y
2
dt
ω=
dθ
dt
α=
dω d θ
= 2
dt
dt
y = A cos ω t or y = A sin ωt
2
v = ±ω
( A2 − y 2 )
ω = ωo + αt
Ek = 12 mω 2 A2 − y 2
θ = ωo t + 12 αt 2
E p = 12 mω 2 y 2
(
ω2 = ωo2 + 2αθ
λ=
s = rθ
v = rω
h
p
mvr =
at = rα
nh
2π
Q1Q2
v2
= rω 2
ar =
r
F=
mv 2
= mrω 2
F=
r
E=
Q
4πε o r 2
T = Fr
V=
Q
4πε o r
T = Iα
4πε o r 2
F = QE
L = mvr = mr ω
2
6
)
Relationships for Advanced Higher
V = Ed
optical path difference = mλ
F = IlBsinθ
optical path difference = (m + 12 )λ
B=
μo I
2π r
Δx =
λ
4n
F μo I1I 2
=
l
2π r
d=
F = qvB
Δx =
ε = − L dI
λD
d
n = tan i p
dt
E = 12 LI 2
2
ΔX
⎛ ΔY ⎞ ⎛ ΔZ ⎞
= ⎜
⎟ +⎜
⎟
X
⎝ Y ⎠ ⎝ Z ⎠
x⎞
⎛
y = A sin 2π ⎜ ft − ⎟
λ⎠
⎝
Δ X = ΔY 2 + ΔZ 2
⎛ v ⎞
f = fs ⎜
⎟
⎝ v ± vs ⎠
Δm =
⎛ v ± vo ⎞
f = fs ⎜
⎟
⎝ v ⎠
Δc =
Φ=
λl
2d
2π x
λ
7
m1 − m2
2 ( n − 2)
c1 − c2
2 ( n − 2)
2
Additional Relationships
Circle
Table of standard derivatives
circumference = 2πr
area = πr
f (x)
f '(x)
sinax
acosax
cosax
– asinax
2
Sphere
area = 4πr 2
Table of standard integrals
volume = 43 πr 3
f (x)
Trigonometry
sin θ =
sinax
opposite
hypotenuse
cos θ =
adjacent
hypotenuse
tan θ =
opposite
adjacent
cosax
sin 2 θ + cos2 θ = 1
Moment of inertia
point mass
I = mr 2
rod about centre
1
I = 12
ml 2
rod about end
I = 13 ml 2
disc about centre
I = 12 mr 2
sphere about centre
I = 25 mr 2
8
∫ f (x)dx
1
cosax + C
a
1
sinax + C
a
Electron Arrangements of Elements
Group Group
1
Group Group Group Group Group Group
4
3
2
5
7
6
0
(1)
(18)
Key
1
2
Atomic number
Symbol
Electron arrangement
Name
H
1
Hydrogen
(2)
He
2
(13)
(14)
(15)
(16)
(17)
Helium
5
6
7
8
9
10
Ne
3
4
Li
Be
B
C
N
O
F
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
2, 7
2, 8
Lithium
Beryllium
Boron
Carbon
Nitrogen
Oxygen
Fluorine
Neon
13
14
15
16
17
18
Transition Elements
11
12
Na
Mg
2, 8, 1
2, 8, 2
Sodium
Magnesium
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Al
Si
P
S
Cl
Ar
2, 8, 3
2, 8, 4
2, 8, 5
2, 8, 6
2, 8, 7
2, 8, 8
Aluminium
Silicon
Phosphorus
Sulphur
Chlorine
Argon
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
9
2, 8, 8, 1
2, 8, 8, 2
2, 8, 9, 2
2, 8, 10, 2
2, 8, 11, 2
2, 8, 13, 1
2, 8, 13, 2
2, 8, 14, 2
2, 8, 15, 2
2, 8, 16, 2
2, 8, 18, 1
2, 8, 18, 2
2, 8, 18, 3
2, 8, 18, 4
2, 8, 18, 5
2, 8, 18, 6
2, 8, 18, 7
2, 8, 18, 8
Potassium
Calcium
Scandium
Titanium
Vanadium
Chromium
Manganese
Iron
Cobalt
Nickel
Copper
Zinc
Gallium
Germanium
Arsenic
Selenium
Bromine
Krypton
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
2, 8, 18, 8, 1
2, 8, 18, 8, 2
Rubidium
Strontium
2, 8, 18, 9, 2 2, 8, 18, 10, 2 2, 8, 18, 12, 1 2, 8, 18, 13, 1 2, 8, 18, 13, 2 2, 8, 18, 15, 1 2, 8, 18, 16, 1 2, 8, 18, 18, 0 2, 8, 18, 18, 1 2, 8, 18, 18, 2
Yttrium
Zirconium
Niobium
Molybdenum Technetium
Ruthenium
Rhodium
Palladium
Silver
2, 8, 18, 18, 3 2, 8, 18, 18, 4 2, 8, 18, 18, 5 2, 8, 18, 18, 6 2, 8, 18, 18, 7 2, 8, 18, 18, 8
Cadmium
Indium
Antimony
Tin
Tellurium
Xenon
Iodine
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
2, 8, 18, 18,
8, 1
Caesium
2, 8, 18, 18,
8, 2
Barium
2, 8, 18, 18,
9, 2
Lanthanum
2, 8, 18, 32,
10, 2
Hafnium
2, 8, 18, 32,
11, 2
Tantalum
2, 8, 18, 32,
12, 2
Tungsten
2, 8, 18, 32,
13, 2
Rhenium
2, 8, 18, 32,
14, 2
Osmium
2, 8, 18, 32,
15, 2
Iridium
2, 8, 18, 32,
17, 1
Platinum
2, 8, 18, 32,
18, 1
Gold
2, 8, 18, 32,
18, 2
Mercury
2, 8, 18, 32,
18, 3
Thallium
2, 8, 18, 32,
18, 4
Lead
2, 8, 18, 32,
18, 5
Bismuth
2, 8, 18, 32,
18, 6
Polonium
2, 8, 18, 32,
18, 7
Astatine
2, 8, 18, 32,
18, 8
Radon
87
88
89
104
105
106
107
108
109
Fr
Ra
Ac
Rf
Db
Sg
Bh
Hs
Mt
2, 8, 18, 32,
18, 8, 1
Francium
2, 8, 18, 32,
18, 8, 2
Radium
2, 8, 18, 32,
32, 12, 2
Seaborgium
2, 8, 18, 32,
32, 13, 2
Bohrium
2, 8, 18, 32,
32, 14, 2
Hassium
2, 8, 18, 32,
32, 15, 2
Meitnerium
2, 8, 18, 32, 2, 8, 18, 32, 2, 8, 18, 32,
32, 10, 2
18, 9, 2
32, 11, 2
Actinium Rutherfordium Dubnium
Lanthanides
Actinides
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
La
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
Lu
2, 8, 18, 25,
8, 2
Europium
2, 8, 18, 25,
9, 2
Gadolinium
2, 8, 18, 27,
8, 2
Terbium
2, 8, 18, 28,
8, 2
Dysprosium
2, 8, 18, 29,
8, 2
Holmium
2, 8, 18, 30,
8, 2
Erbium
2, 8, 18, 31,
8, 2
Thulium
2, 8, 18, 32,
8, 2
Ytterbium
2, 8, 18, 32,
9, 2
Lutetium
2, 8, 18, 18,
9, 2
Lanthanum
2, 8, 18, 20, 2, 8, 18, 21, 2, 8, 18, 22, 2, 8, 18, 23, 2, 8, 18, 24,
8, 2
8, 2
8, 2
8, 2
8, 2
Cerium
Praseodymium Neodymium Promethium Samarium
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
Ac
Th
Pa
U
Np
Pu
Am
Cm
Bk
Cf
Es
Fm
Md
No
Lr
2, 8, 18, 32,
22, 9, 2
Neptunium
2, 8, 18, 32,
24, 8, 2
Plutonium
2, 8, 18, 32,
25, 8, 2
Americium
2, 8, 18, 32,
25, 9, 2
Curium
2, 8, 18, 32,
27, 8, 2
Berkelium
2, 8, 18, 32,
18, 9, 2
Actinium
2, 8, 18, 32, 2, 8, 18, 32, 2, 8, 18, 32,
18, 10, 2
20, 9, 2
21, 9, 2
Thorium Protactinium Uranium
2, 8, 18, 32, 2, 8, 18, 32,
28, 8, 2
29, 8, 2
Californium Einsteinium
2, 8, 18, 32, 2, 8, 18, 32, 2, 8, 18, 32, 2, 8, 18, 32,
30, 8, 2
31, 8, 2
32, 8, 2
32, 9, 2
Fermium Mendelevium Nobelium Lawrencium