Physics
First examinations 2009
Diploma Programme
Data booklet
Diploma Programme
Physics
Data booklet
First examinations 2009
International Baccalaureate Organization
Buenos Aires
Cardiff
Geneva
New York
Singapore
Diploma Programme
Physics—data booklet
Published September 2007
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© International Baccalaureate Organization 2007
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Contents
Fundamental constants
1
Metric (SI) multipliers
2
Unit conversions
3
Electrical circuit symbols
4
Equations—Core and AHL
5
Equations—Options SL
11
Equations—Options SL and HL
13
Equations—Options HL
15
Physics data booklet
Fundamental constants
Quantity
Symbol
Approximate value
Acceleration of free fall
(Earth’s surface)
g
9.81m s !2
Gravitational constant
G
6.67 "10!11 N m 2 kg !2
Avogadro’s constant
NA
6.02 "1023 mol!1
Gas constant
R
8.31J K !1 mol !1
Boltzmann’s constant
k
1.38 "10!23 J K !1
Stefan–Boltzmann constant
#
5.67 "10!8 W m !2 K !4
Coulomb constant
k
8.99 "109 N m 2 C!2
Permittivity of free space
$0
8.85 "10!12 C2 N !1 m !2
Permeability of free space
%0
4! " 10!7 T m A !1
Speed of light in vacuum
c
3.00 "108 m s !1
Planck’s constant
h
6.63 "10!34 J s
Elementary charge
e
1.60 "10!19 C
Electron rest mass
me
9.110 "10!31 kg & 0.000549 u & 0.511MeV c !2
Proton rest mass
mp
1.673 "10!27 kg & 1.007276 u & 938 MeV c !2
Neutron rest mass
mn
1.675 "10!27 kg & 1.008665 u & 940 MeV c !2
Unified atomic mass unit
u
1.661"10!27 kg & 931.5 MeV c !2
© International Baccalaureate Organization 2007
1
Physics data booklet
Metric (SI) multipliers
2
Prefix
Abbreviation
Value
tera
T
1012
giga
G
109
mega
M
106
kilo
k
103
hecto
h
102
deca
da
101
deci
d
10–1
centi
c
10–2
milli
m
10–3
micro
µ
10–6
nano
n
10–9
pico
p
10–12
femto
f
10–15
© International Baccalaureate Organization 2007
Physics data booklet
Unit conversions
1 light year (ly) & 9.46 "1015 m
1 parsec (pc) & 3.26 ly
1 astronomical unit (AU) & 1.50 "1011 m
1 radian (rad) &
180'
!
1 kilowatt-hour (kW h) & 3.60 " 106 J
1 atm & 1.01"105 N m !2 & 101kPa & 760 mm Hg
© International Baccalaureate Organization 2007
3
Physics data booklet
Electrical circuit symbols
cell
battery
lamp
ac supply
switch
ammeter
voltmeter
V
A
variable resistor
resistor
potentiometer
light-dependent
resistor (LDR)
thermistor
transformer
heating element
operational
amplifier
(op-amp)
4
© International Baccalaureate Organization 2007
Physics data booklet
Equations—Core and AHL
Note: All equations relate to the magnitude of the quantities only. Vector notation has not been used.
Core
AHL
Topic 1: Physics and physical
measurement
If y & a ( b
then )y & )a * )b
If y &
ab
c
then
)y )a )b )c
&
*
*
y
a
b
c
A
AV
"
AH
AH & A cos +
AV & A sin +
© International Baccalaureate Organization 2007
5
Equations—Core and AHL
Core
AHL
Topic 2: Mechanics
s&
u*v
t
2
s & ut * 12 at 2
v 2 & u 2 * 2as
F & ma
p & mv
F&
)p
)t
Impulse & F )t & m)v
W & Fs cos +
EK & 12 mv 2
EK &
p2
2m
)EP & mg )h
power & Fv
a&
v 2 4! 2 r
& 2
r
T
Topic 3: Thermal physics
P&
F
A
Q & mc)T
Topic 10: Thermal physics
PV & nRT
W & P )V
Q & )U * W
Q & mL
6
© International Baccalaureate Organization 2007
Equations—Core and AHL
Core
AHL
Topic 4: Oscillations and waves
2!
T
Topic 11: Wave phenomena
0 v 1
f2 & f 3
4
5 v ( us 6
moving source
v & v0 cos ,t ; v & !v0 sin ,t
0 v ( uo 1
f2& f 3
4
5 v 6
moving observer
v & (, ( x0 2 ! x 2 )
)f &
,&
x & x0 sin , t ; x & x0 cos , t
EK & 12 m, 2 ( x0 2 ! x 2 )
EK (max) & 12 m, 2 x0 2
+&
v
f
c
b
-
ET & 12 m, 2 x0 2
+ & 1.22
v& f-
I & I 0 cos 2 +
n1 sin + 2 v2
&
&
n2 sin +1 v1
b
n & tan7
path difference & npath difference & . n * 12 / -
© International Baccalaureate Organization 2007
7
Equations—Core and AHL
Core
AHL
Topic 5: Electric currents
Topic 12: Electromagnetic induction
Ve & 12 mv 2
: & BA cos +
I&
)q
)t
R&
V
I
R&
$ & Bvl
$ & ! N ):
)t
I s Vp N p
& &
I p Vs N s
8L
A
P & VI & I 2 R &
V
R
2
$ & I .R * r/
I rms &
I0
2
Vrms &
V0
2
V0 Vrms
&
I 0 I rms
R & R1 * R2 * 999
R&
1 1
1
& * * 999
R R1 R2
Pmax & I 0V0
Pav & 12 I 0V0
Topic 6: Fields and forces
F &G
m1m2
r2
g&
F
m
F&
q1q2
4!!0 r 2
F &k
E&
F
q
Topic 9: Motion in fields
q1q2
r2
)V &
)Ep
m
)V &
V &!
Gm
r
V&
g&!
)V
)r
E&!
)Ep
q
kq
q
&
r 4;$ 0 r
)V
)x
F & qvB sin +
F & BIL sin +
8
© International Baccalaureate Organization 2007
Equations—Core and AHL
Core
Topic 7: Atomic and nuclear physics
E = mc2
AHL
Topic 13: Quantum physics and nuclear
physics
E & hf
hf & 7 * Emax
hf & hf 0 * eV
p&
h
-
EK &
n2 h2
8me L2
)x )p <
h
4;
)E )t <
h
4;
N & N 0 e ! -t
A&!
#N
#t
A & - N & - N 0 e ! -t
T1 &
2
© International Baccalaureate Organization 2007
ln 2
-
9
Equations—Core and AHL
Core
AHL
Topic 8: Energy, power and climate
change
power & 12 A8 v3
power per unit length & 12 A2 8 gv
I&
power
A
albedo &
Cs &
total scattered power
total incident power
Q
A)T
power & # AT 4
power & e # AT 4
)T &
10
. Iin ! I out / )t
Cs
© International Baccalaureate Organization 2007
Physics data booklet
Equations—Options SL
Option A: Sight and wave phenomena
0 v 1
f2& f 3
4
5 v ( us 6
0 v ( uo 1
f2& f 3
4
5 v 6
moving source
moving observer
v
)f & f
c
+&
b
+ & 1.22
b
I & I 0 cos 2 +
n & tan 7
Option B: Quantum physics and nuclear physics
E & hf
)E )t <
hf & 7 * Emax
hf & hf 0 * eV
p&
N & N 0 e ! -t
A&!
h
-
n2 h2
EK &
8me L2
h
)x )p <
4;
h
4;
#N
#t
A & - N & - N 0 e ! -t
T1 &
2
ln 2
-
Option C: Digital technology
G&!
RF
R
G & 1*
RF
R
© International Baccalaureate Organization 2007
11
Equations—Options SL
Option D: Relativity and particle physics
1
=&
1!
v2
c2
)t & = ) t0
L&
12
L0
)E )t <
R>
h
4!
h
4!mc
E & hf
=
© International Baccalaureate Organization 2007
Physics data booklet
Equations—Options SL and HL
Core (SL and HL)
Extension (HL only)
Option E: Astrophysics
L & # AT 4
L ? mn
-max (metres) &
d . parsec / &
b&
2.90 "10!3
T (kelvin)
1
p . arc-second /
)-
-
A
where 3 @ n @ 4
v
c
v & H 0d
L
4!d 2
0d 1
m ! M & 5lg 3 4
5 10 6
Option F: Communications
n&
1
sin C
attenuation / dB & 10 lg
G&!
I1
I2
© International Baccalaureate Organization 2007
RF
R
G & 1*
RF
R
13
Equations—Options SL and HL
Core (SL and HL)
Extension (HL only)
Option G: Electromagnetic waves
1 1 1
& *
f v u
-min &
2d sin + & n-
P&
1
f
m&
hi
v
&!
ho
u
2nt & m-
M&
f
M& o
fe
m&
s&
hc
eV
+i
+o
2nt & . m * 12 / -
2nt cos 7 & m2nt cos 7 & . m * 12 / -
D
*1
f
m&
D
f
-D
d
sin + &
nd
x n&
D d
x
& (n+ 12 )
D
d
d sin + & n-
14
© International Baccalaureate Organization 2007
Physics data booklet
Equations—Options HL
Option H: Relativity
EK & .= ! 1/ m0 c 2
1
=&
1!
v2
c2
E 2 & p 2 c 2 * m02c 4
)t & = ) t0
L&
)f g )h
& 2
f
c
L0
=
u x2 &
ux ! v
uv
1 ! x2
c
Rs &
E0 & m0c 2
)t &
E & = m0c 2
2GM
c2
)t0
R
1! s
r
p & = m0u
Option I: Medical physics
IL & 10 lg
I & I 0e
I
I0
where I 0 & 1.0 " 10!12 W m !2
!% x
Z & 8c
1
1 1
& *
TE TP TB
% x & ln 2
1
2
dose equivalent = absorbed dose × quality factor
© International Baccalaureate Organization 2007
15
Equations—Options HL
Option J: Particle physics
)E )t <
h
4!
h
R>
4!mc
E & hf
Ea2 & 2 Mc 2 E * ( Mc 2 ) 2 * (mc 2 ) 2
-&
h
p
EK & 32 kT
E & mc 2 * EK
16
© International Baccalaureate Organization 2007