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
International Baccalaureate Organization
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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
g 9.81ms-2
(Earth s surface)
Gravitational constant G 6.67�10-11 N m2 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 m2 C-2
�0
Permittivity of free space 8.85�10-12 C2 N-1 m-2
ź0
Permeability of free space 4Ą�10-7 T m A-1
Speed of light in vacuum c 3.00�108 ms-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 = 938MeV c-2
Neutron rest mass mn 1.675�10-27 kg = 1.008665u = 940 MeV c-2
Unified atomic mass unit u 1.661�10-27 kg = 931.5MeV c-2
� International Baccalaureate Organization 2007 1
Physics data booklet
Metric (SI) multipliers
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 � 10 6
nano n 10 9
pico p 10 12
femto f 10 15
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Physics data booklet
Unit conversions
1 light year (ly) = 9.46�1015 m
1 parsec (pc) = 3.26ly
1 astronomical unit (AU) =1.50�1011 m
180�
1 radian (rad) =
Ą
1 kilowatt-hour (kW h) = 3.60�106 J
1 atm = 1.01�105 N m-2 =101kPa = 760 mm Hg
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Physics data booklet
Electrical circuit symbols
cell battery
lamp ac supply
A
switch ammeter
voltmeter V variable resistor
resistor potentiometer
light-dependent
thermistor
resistor (LDR)
transformer heating element
operational
amplifier
(op-amp)
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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 ą b
then "y = "a + "b
ab
If y =
c
"y "a "b "c
then = + +
y a b c
AV A
�
AH
AH = Acos�
AV = Asin�
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Equations Core and AHL
Core AHL
Topic 2: Mechanics
u + v
s = t
2
1
s = ut + at2
2
v2 = u2 + 2as
F = ma
p = mv
"p
F =
"t
Impulse = F"t = m"v
W = Fs cos�
1
EK = mv2
2
p2
EK =
2m
"EP = mg"h
power = Fv
v2 4Ą2r
a = =
2
r T
Topic 3: Thermal physics Topic 10: Thermal physics
F PV = nRT
P =
A
W = P"V
Q = mc"T
Q = "U +W
Q = mL
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Equations Core and AHL
Core AHL
Topic 4: Oscillations and waves Topic 11: Wave phenomena
2Ą
�# ś#
v
� =
2
f = f moving source
ś# ź#
T
v ą us
�# #
x = x0 sin�t ; x = x0 cos�t
v ą uo
�# ś#
2
f = f moving observer
ś# ź#
v = v0 cos�t ; v = -v0 sin�t v
�# #
v
v =ą� (x02 - x2)
"f = f
c
1
EK = m�2(x02 - x2)
2

� =
1 b
EK(max) = m�2x02
2

2
1
� = 1.22
ET = m� x02
2
b
v = f 
I = I0 cos2 �
n1 sin�2 v2
n = tanĆ
= =
n2 sin�1 v1
path difference = n
1
path difference = n + 
( )
2
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Equations Core and AHL
Core AHL
Topic 5: Electric currents Topic 12: Electromagnetic induction
1
Ve = mv2
2
Ś = BAcos�
� = Bvl
"q
I =
"t "Ś
� =-N
"t
V
R =
I
Is Vp Np
= =
Ip Vs Ns
�L
R =
A
I0
Irms =
2
V
2 2
P = VI = I R =
R
V0
Vrms =
2
� = I R + r
( )
V0 Vrms
R = R1 + R2 +�"�"�"
R = =
I0 Irms
1 1 1
= + +�"�"�"
Pmax = I0V0
R R1 R2
1
Pav = I0V0
2
Topic 6: Fields and forces Topic 9: Motion in fields
"Ep "Ep
mm2 qq2
"V = "V =
1 1
F = G F = k
m q
r2 r2
F F
Gm kq q
g = E =
V =- V = =
m q
r r 4Ą�0r
qq2
1
"V "V
F =
g =- E =-
4Ą�0r2
"r "x
F = qvB sin�
F = BIL sin�
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Equations Core and AHL
Core AHL
Topic 7: Atomic and nuclear physics Topic 13: Quantum physics and nuclear
physics
E = mc2
E = hf
hf = Ć + Emax
hf = hf0 + eV
h
p =

n2h2
EK =
8mL2
e
h
"x "p e"
4Ą
h
"E "t e"
4Ą
N = N0e-t
"N
A =-
"t
A = N = N0e-t
ln 2
T =
1
2

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Equations Core and AHL
Core AHL
Topic 8: Energy, power and climate
change
1
power = A�v3
2
1
power per unit length = A2� gv
2
power
I =
A
total scattered power
albedo =
total incident power
Q
Cs =
A"T
4
power = � AT
4
power = e� AT
Iin
( - Iout "t
)
"T =
Cs
10 � International Baccalaureate Organization 2007
Physics data booklet
Equations Options SL
Option A: Sight and wave phenomena

�# ś#
v
� =
2
f = f moving source
ś# ź#
b
v ą us
�# #

v ą uo � = 1.22
�# ś#moving observer
2
f = f
b
ś# ź#
v
�# #
I = I0 cos2 �
v
"f = f
n = tanĆ
c
Option B: Quantum physics and nuclear physics
E = hf h
"E "t e"
4Ą
hf = Ć + Emax
N = N0e-t
hf = hf0 + eV
"N
A =-
h
p =
"t

A = N = N0e-t
n2h2
EK =
ln 2
8mL2
e
T =
1
2

h
"x "p e"
4Ą
Option C: Digital technology
RF
G =-
R
RF
G =1+
R
� International Baccalaureate Organization 2007 11
Equations Options SL
Option D: Relativity and particle physics
1 h
ł = "E "t e"
4Ą
v2
1-
c2
h
R H"
4Ąmc
"t = ł" t0
E = hf
L0
L =
ł
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Physics data booklet
Equations Options SL and HL
Core (SL and HL) Extension (HL only)
Option E: Astrophysics
4
L = � AT L " mn where 3 < n < 4
2.90�10-3 " v
max (metres) = E"
T (kelvin)  c
v = H0d
1
d parsec =
( )
p arc-second
()
L
b =
2
4Ąd
d
�# ś#
m - M = 5lg
ś#10 ź#
�# #
Option F: Communications
1 RF
n = G =-
sin C R
I1 RF
attenuation / dB = 10lg G =1+
I2 R
� International Baccalaureate Organization 2007 13
Equations Options SL and HL
Core (SL and HL) Extension (HL only)
Option G: Electromagnetic waves
1 1 1 hc
= + min =
f v u eV
2d sin� = n
1
P =
f
2nt = m
1
hi v �i
2nt = m + 
( )
2
m = = - M =
ho u �o
2nt cosĆ = m
fo
1
M =
2nt cosĆ = m + 
( )
2
fe
D D
m = +1 m =
f f
D
s =
d
n
sin� =
d
x n
=
D d
x 
1
= (n+ )
2
Dd
d sin� = n
14 � International Baccalaureate Organization 2007
Physics data booklet
Equations Options HL
Option H: Relativity
1
EK = ł -1 m0c2
( )
ł =
v2
1-
c2
2
E2 = p2c2 + m0c4
"t = ł "t0
L0 "f g"h
L = =
ł f c2
ux - v
ux2 =
2GM
uxv
Rs =
1-
c2
c2
"t0
E0 = m0c2 "t =
Rs
1-
r
E = ł m0c2
p = ł mu
0
Option I: Medical physics
I
Z = �c
IL =10lg where I0 =1.0�10-12 W m-2
I0
1 1 1
= +
TE TP TB
I = I0e-ź x
ź x = ln 2
1
2
dose equivalent = absorbed dose � quality factor
� International Baccalaureate Organization 2007 15
Equations Options HL
Option J: Particle physics
2
h
Ea = 2Mc2E + (Mc2)2 + (mc2)2
"E "t e"
4Ą
h
 =
h
p
R H"
4Ąmc
3
EK = kT
2
E = hf
E = mc2 + EK
16 � International Baccalaureate Organization 2007