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Physics Data Booklet

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Physics data booklet
First assessment 2016
Diploma Programme
Physics data booklet
Published February 2014
Published on behalf of the International Baccalaureate Organization, a not-for-profit
educational foundation of 15 Route des Morillons, 1218 Le Grand-Saconnex, Geneva,
Switzerland by the
International Baccalaureate Organization (UK) Ltd
Peterson House, Malthouse Avenue, Cardiff Gate
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United Kingdom
Website: www.ibo.org
© International Baccalaureate Organization 2014
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4082
Contents
Fundamental constants
1
Metric (SI) multipliers
2
Unit conversions
3
Electrical circuit symbols
4
Equations—Core
5
Equations—AHL
8
Equations—Options
10
Physics data booklet
Fundamental constants
Quantity
Acceleration of free fall (Earth’s surface)
Gravitational constant
Symbol
g
G
Avogadro’s constant
𝑁A
Boltzmann’s constant
π‘˜B
Coulomb constant
k
Gas constant
Stefan–Boltzmann constant
Permittivity of free space
R
σ
πœ€0
Permeability of free space
πœ‡0
Planck’s constant
h
Electron rest mass
π‘še
Speed of light in vacuum
Elementary charge
Proton rest mass
Neutron rest mass
Unified atomic mass unit
Solar constant
Fermi radius
Physics data booklet
c
e
π‘šp
π‘šn
u
S
𝑅0
Approximate value
9.81 m s−2
6.67 × 10−11 N m2 kg−2
6.02 × 1023 mol−1
8.31 J K−1 mol−1
1.38 × 10−23 J K−1
5.67 × 10−8 W m−2 K−4
8.99 × 109 N m2 C−2
8.85 × 10−12 C2 N−1 m−2
4π × 10−7 T m A−1
3.00 × 108 m s−1
6.63 × 10−34 J s
1.60 × 10−19 C
9.110 × 10−31 kg = 0.000549 u = 0.511 MeV c−2
1.673 × 10−27 kg =1.007276 u = 938 MeV c−2
1.675 × 10−27 kg =1.008665 u = 940 MeV c−2
1.661 × 10−27 kg = 931.5 MeV c−2
1.36 × 103 W m−2
1.20 × 10−15 m
1
Metric (SI) multipliers
Prefix
Abbreviation
Value
peta
P
1015
G
109
tera
T
mega
M
hecto
h
giga
kilo
k
deca
da
centi
c
deci
1012
106
103
102
101
d
10–1
milli
m
10–3
nano
n
micro
pico
femto
Physics data booklet
µ
p
f
10–2
10–6
10–9
10–12
10–15
2
Unit conversions
1 radian (rad) ≡
180°
π
Temperature (K) = temperature (°C) + 273
1 light year (ly) = 9.46 × 1015 m
1 parsec (pc) = 3.26 ly
1 astronomical unit (AU) =1.50 × 1011 m
1 kilowatt-hour (kWh) = 3.60 × 106 J
hc = 1.99 × 10-25 J m = 1.24 × 10–6 eV m
Physics data booklet
3
Electrical circuit symbols
cell
battery
ac supply
switch
voltmeter
V
ammeter
resistor
variable resistor
lamp
potentiometer
light-dependent resistor
(LDR)
thermistor
transformer
heating element
diode
capacitor
Physics data booklet
A
4
Equations—Core
Note: All equations relate to the magnitude of the quantities only. Vector notation has not been used.
Sub-topic 1.2 – Uncertainties and errors
Sub-topic 1.3 – Vectors and scalars
If: 𝑦 = π‘Ž ± 𝑏
then: π›₯𝑦 = π›₯π‘Ž + π›₯𝑏
π‘Žπ‘
𝑐
π›₯𝑦 π›₯π‘Ž π›₯𝑏 π›₯𝑐
then:
=
+
+
𝑦
π‘Ž
𝑏
𝑐
If: 𝑦 =
If: 𝑦 = π‘Žπ‘›
then:
βˆ†π‘¦
βˆ†π‘Ž
= �𝑛 οΏ½
𝑦
π‘Ž
Sub-topic 2.1 – Motion
𝐴H = 𝐴 cos πœƒ
𝐴V = 𝐴 sin πœƒ
Sub-topic 2.2 – Forces
𝑣 = 𝑒 + π‘Žπ‘‘
𝐹 = π‘šπ‘Ž
𝑣 2 = 𝑒2 + 2π‘Žπ‘ 
𝐹f = πœ‡d 𝑅
1
2
𝑠 = 𝑒𝑑 + π‘Žπ‘‘ 2
𝑠=
(𝑣 + 𝑒)𝑑
2
𝐹f ≤ πœ‡s 𝑅
Sub-topic 2.3 – Work, energy and power
Sub-topic 2.4 – Momentum and impulse
π‘Š = 𝐹𝑠 π‘π‘œπ‘ πœƒ
𝑝 = π‘šπ‘£
1
𝐸K = 2 π‘šπ‘£ 2
1
𝐸P = 2 π‘˜βˆ†π‘₯ 2
βˆ†πΈP = π‘šπ‘”βˆ†β„Ž
power = 𝐹𝑣
useful work out
total work in
useful power out
=
total power in
EfοΏ½iciency =
Physics data booklet
𝐹=
βˆ†π‘
βˆ†π‘‘
𝐸K =
𝑝2
2π‘š
Impulse = πΉβˆ†π‘‘ = βˆ†π‘
5
Sub-topic 3.1 – Thermal concepts
𝑄 = π‘šπ‘βˆ†π‘‡
𝑄 = π‘šπΏ
Sub-topic 3.2 – Modelling a gas
𝐹
𝐴
𝑁
𝑛=
𝑁A
𝑝=
𝑝𝑉 = 𝑛𝑅𝑇
3
3
𝐸�K = 2 π‘˜B 𝑇 = 2
Sub-topic 4.1 – Oscillations
𝑇=
1
𝑓
Sub-topic 4.2 – Travelling waves
𝑐 = π‘“πœ†
Sub-topic 4.3 – Wave characteristics
𝐼 ∝ 𝐴2
𝐼 ∝ π‘₯ −2
𝐼 = 𝐼0 π‘π‘œπ‘  2 πœƒ
𝑅
𝑇
𝑁A
Sub-topic 4.4 – Wave behaviour
𝑛1 sin πœƒ2 𝑣2
=
=
𝑛2 sin πœƒ1 𝑣1
𝑠=
πœ†π·
𝑑
Constructive interference: path difference = π‘›πœ†
Destructive interference:
1
path difference = (𝑛 + 2)πœ†
Sub-topic 5.1 – Electric fields
Sub-topic 5.2 – Heating effect of electric currents
βˆ†π‘ž
βˆ†π‘‘
π‘ž1 π‘ž2
𝐹=π‘˜ 2
π‘Ÿ
1
π‘˜=
4πœ‹πœ€0
Kirchhoff’s circuit laws:
𝐼=
𝑉=
𝐸=
π‘Š
π‘ž
𝐹
π‘ž
𝐼 = π‘›π΄π‘£π‘ž
Σ𝑉 = 0 (loop)
𝑅=
Σ𝐼 = 0 (junction)
𝑉
𝐼
𝑃 = 𝑉𝐼 = 𝐼 2 𝑅 =
𝑅total = 𝑅1 + 𝑅2 + β‹―
1
𝑅total
=
𝑅𝐴
𝐿
1
1
+
+β‹―
𝑅1 𝑅2
Sub-topic 5.3 – Electric cells
𝜌=
πœ€ = 𝐼(𝑅 + π‘Ÿ)
𝐹 = π‘žπ‘£π΅ sin πœƒ
Physics data booklet
𝑉2
𝑅
Sub-topic 5.4 – Magnetic effects of electric currents
𝐹 = 𝐡𝐼𝐿 sin πœƒ
6
Sub-topic 6.1 – Circular motion
Sub-topic 6.2 – Newton’s law of gravitation
𝑣 = πœ”π‘Ÿ
π‘Ž=
𝐹=
𝑣 2 4πœ‹ 2 π‘Ÿ
= 2
π‘Ÿ
𝑇
𝐹=𝐺
π‘€π‘š
π‘Ÿ2
𝑔=𝐺
𝑀
π‘Ÿ2
𝑔=
π‘šπ‘£ 2
= π‘šπœ”2 π‘Ÿ
π‘Ÿ
𝐹
π‘š
Sub-topic 7.1 – Discrete energy and radioactivity
Sub-topic 7.2 – Nuclear reactions
𝐸 = β„Žπ‘“
βˆ†πΈ = βˆ†π‘š 𝑐 2
πœ†=
β„Žπ‘
𝐸
Sub-topic 7.3 – The structure of matter
Charge
2
𝑒
3
Quarks
u
1
− 𝑒
3
d
c
s
Baryon
number
t
b
Charge
–1
1
3
0
1
3
Particles mediating
e
υe
µ
τ
υµ
υτ
All leptons have a lepton number
of 1 and antileptons have a lepton
number of –1
All quarks have a strangeness number of 0
except the strange quark that has a
strangeness number of –1
Particles experiencing
Leptons
Gravitational
Weak
Electromagnetic
Strong
All
Quarks, leptons
Charged
Quarks, gluons
Graviton
W+,
W–,
Z0
γ
Sub-topic 8.1 – Energy sources
Sub-topic 8.2 – Thermal energy transfer
energy
Power =
time
𝑃 = π‘’πœŽπ΄π‘‡ 4
1
Power = 2 π΄πœŒπ‘£ 3
Physics data booklet
πœ†max (metres) =
Gluons
2.90 × 10−3
𝑇(kelvin)
power
𝐴
total scattered power
albedo =
total incident power
𝐼=
7
Equations—AHL
Sub-topic 9.1 – Simple harmonic motion
πœ”=
2πœ‹
𝑇
Sub-topic 9.2 – Single-slit diffraction
πœƒ=
π‘Ž = −πœ”2 π‘₯
πœ†
𝑏
Sub-topic 9.3 – Interference
π‘₯ = π‘₯0 sin πœ”π‘‘ ; π‘₯ = π‘₯0 cos πœ”π‘‘
π‘›πœ† = 𝑑 sin πœƒ
𝑣 = ±πœ”οΏ½(π‘₯0 2 − π‘₯ 2 )
Destructive interference:
𝑣 = πœ”π‘₯0 cos πœ”π‘‘ ; 𝑣 = −πœ”π‘₯0 sin πœ”π‘‘
𝐸K =
1
2
1
π‘šπœ”2 (π‘₯0 2
𝐸T = 2 π‘šπœ”2 π‘₯0 2
−π‘₯
2)
1
Constructive interference: 2𝑑𝑛 = (π‘š + 2) πœ†
2𝑑𝑛 = π‘šπœ†
𝑙
Pendulum: 𝑇 = 2πœ‹οΏ½
𝑔
π‘š
Mass–spring: 𝑇 = 2πœ‹οΏ½
π‘˜
Sub-topic 9.4 – Resolution
πœƒ = 1.22
𝑅=
πœ†
𝑏
πœ†
= π‘šπ‘
Δπœ†
Sub-topic 10.1 – Describing fields
Sub-topic 9.5 – Doppler effect
𝑣
Moving source: 𝑓 ′ = 𝑓 οΏ½
οΏ½
𝑣 ± 𝑒s
Moving observer: 𝑓 ′ = 𝑓 οΏ½
βˆ†π‘“ βˆ†πœ† 𝑣
=
≈
𝑓
πœ†
𝑐
𝑣±π‘’0
𝑣
οΏ½
Sub-topic 10.2 – Fields at work
π‘Š = π‘žβˆ†π‘‰π‘’
π‘Š = π‘šβˆ†π‘‰π‘”
𝑉𝑔 = −
𝑔=−
𝐺𝑀
π‘Ÿ
Δ𝑉𝑔
Δπ‘Ÿ
𝐸P = π‘šπ‘‰π‘” = −
𝐹G = 𝐺
𝑣esc = οΏ½
2𝐺𝑀
π‘Ÿ
πΊπ‘€π‘š
π‘Ÿ
π‘š1 π‘š2
π‘Ÿ2
𝑉𝑒 =
π‘˜π‘ž
π‘Ÿ
𝐸=−
Δ𝑉𝑒
Δπ‘Ÿ
𝐸P = π‘žπ‘‰e =
𝐹E = π‘˜
π‘˜π‘ž1 π‘ž2
π‘Ÿ
π‘ž1 π‘ž2
π‘Ÿ2
𝐺𝑀
𝑣orbit = οΏ½
π‘Ÿ
Physics data booklet
8
Sub-topic 11.1 – Electromagnetic induction
Sub-topic 11.3 – Capacitance
𝛷 = 𝐡𝐴 cos πœƒ
𝐢=
πœ€ = −𝑁
πœ€ = 𝐡𝑣𝑙
βˆ†π›·
Δ𝑑
πœ€ = 𝐡𝑣𝑙𝑁
Sub-topic
11.2
transmission
𝐼rms =
𝑉rms =
𝐢parallel = 𝐢1 + 𝐢2 + β‹―
1
–
Power
generation
and
𝐼0
√2
𝑉0
√2
𝑉0 𝑉rms
𝑅= =
𝐼0 𝐼rms
𝑃max = 𝐼0 𝑉0
1
𝑃� = 2 𝐼0 𝑉0
πœ€p 𝑁p 𝐼s
=
=
πœ€s 𝑁s 𝐼p
π‘ž
𝑉
𝐢series
𝐢=πœ€
𝐸 =
=
𝐴
𝑑
1
1
+ +β‹―
𝐢1 𝐢2
1
𝐢𝑉 2
2
𝜏 = 𝑅𝐢
𝑑
π‘ž = π‘ž0 𝑒 −𝜏
𝑑
𝐼 = 𝐼0 𝑒 −𝜏
𝑑
𝑉 = 𝑉0 𝑒 −𝜏
Sub-topic 12.1 – The interaction of matter with
radiation
Sub-topic 12.2 – Nuclear physics
𝐸 = β„Žπ‘“
𝑅 = 𝑅0 𝐴1/3
13.6
𝑒𝑉
𝑛2
π‘›β„Ž
π‘šπ‘£π‘Ÿ =
2πœ‹
𝐴 = πœ†π‘0 𝑒 −πœ†π‘‘
𝐸max = β„Žπ‘“ − 𝛷
𝐸=−
𝑃(π‘Ÿ) = |ψ|2 Δ𝑉
𝑁 = 𝑁0 𝑒 −πœ†π‘‘
sin πœƒ ≈
πœ†
𝐷
β„Ž
4πœ‹
β„Ž
Δ𝐸Δ𝑑 ≥
4πœ‹
Δπ‘₯Δ𝑝 ≥
Physics data booklet
9
Equations—Options
Sub-topic A.1 – The beginnings of relativity
′
π‘₯ = π‘₯ − 𝑣𝑑
′
𝑒 =𝑒−𝑣
Sub-topic A.3 – Spacetime diagrams
𝑣
πœƒ = tan−1 οΏ½ οΏ½
𝑐
Sub-topic A.2 – Lorentz transformations
𝛾=
1
2
οΏ½1 − 𝑣2
𝑐
π‘₯ ′ = 𝛾(π‘₯ − 𝑣𝑑) ; βˆ†π‘₯ ′ = 𝛾(βˆ†π‘₯ − π‘£βˆ†π‘‘)
𝑑 ′ = 𝛾(𝑑 −
𝑒′ =
𝑣π‘₯
𝑐2
𝑒−𝑣
𝑒𝑣
1− 2
𝑐
) ; βˆ†π‘‘ ′ = 𝛾(βˆ†π‘‘ −
π‘£βˆ†π‘₯
𝑐2
)
βˆ†π‘‘ = π›Ύβˆ†π‘‘0
𝐿=
Sub-topic A.4 – Relativistic mechanics (HL only)
𝐸 = π›Ύπ‘š0 𝑐 2
𝐸0 = π‘š0 𝑐
2
𝐸K = (𝛾 − 1)π‘š0 𝑐 2
𝑝 = π›Ύπ‘š0 𝑣
𝐸 2 = 𝑝2 𝑐 2 + π‘š0 2 𝑐 4
π‘žπ‘‰ = βˆ†πΈK
Physics data booklet
𝐿0
𝛾
(𝑐𝑑 ′ )2 − (π‘₯ ′ )2 = (𝑐𝑑)2 − (π‘₯)2
Sub-topic A.5 – General relativity (HL only)
βˆ†π‘“ π‘”βˆ†β„Ž
= 2
𝑓
𝑐
𝑅s =
βˆ†π‘‘ =
2𝐺𝑀
𝑐2
βˆ†π‘‘0
οΏ½1 − 𝑅s
π‘Ÿ
10
Sub-topic
dynamics
B.1
–
Rigid
bodies
and
rotational
𝛀 = πΉπ‘Ÿ sin πœƒ
𝑄 = βˆ†π‘ˆ + π‘Š
3
𝐼 = ∑π‘šπ‘Ÿ 2
π‘ˆ = 2 𝑛𝑅𝑇
𝛀 = 𝐼𝛼
βˆ†π‘† =
πœ” = 2πœ‹π‘“
πœ”f = πœ” i + 𝛼𝑑
πœ”f2 = πœ”i2 + 2π›Όπœƒ
1
2
πœƒ = πœ”i 𝑑 + 𝛼𝑑
𝐿 = πΌπœ”
2
1
𝐸Krot = 2 πΌπœ”2
Sub-topic B.3 – Fluids and fluid dynamics (HL only)
𝐡 = 𝜌f 𝑉f 𝑔
𝑃 = 𝑃0 + 𝜌f 𝑔𝑑
𝐴𝑣 = constant
1
2
Sub-topic B.2 – Thermodynamics
πœŒπ‘£ 2 + πœŒπ‘”π‘§ + 𝑝 = constant
𝐹D = 6πœ‹πœ‚π‘Ÿπ‘£
π‘£π‘ŸπœŒ
𝑅=
πœ‚
5
βˆ†π‘„
𝑇
𝑝𝑉 3 = constant (for monatomic gases)
π‘Š = π‘βˆ†π‘‰
πœ‚=
useful work done
energy input
πœ‚Carnot = 1 −
𝑇cold
𝑇hot
Sub-topic B.4 – Forced vibrations and resonance
(HL only)
𝑄 = 2πœ‹
energy stored
energy dissipated per cycle
𝑄 = 2πœ‹ × resonant frequency ×
energy stored
power loss
Sub-topic C.1 – Introduction to imaging
Sub-topic C.2 – Imaging instrumentation
1 1 1
= +
𝑓 𝑣 𝑒
𝑀=
𝑃=
1
𝑓
Sub-topic C.3 – Fibre optics
β„Ži
𝑣
π‘š=
=−
β„Žo
𝑒
𝑀=
πœƒi
πœƒo
𝑀near point
𝑓o
𝑓e
𝑛=
1
sin 𝑐
attenuation = 10 log
𝐼
𝐼0
Sub-topic C.4 – Medical imaging (HL only)
𝐷
𝐷
= + 1 ; 𝑀inοΏ½inity =
𝑓
𝑓
𝐿I = 10 log
𝐼 = 𝐼0 𝑒 −πœ‡π‘₯
𝐼1
𝐼0
πœ‡π‘₯1 = ln2
2
𝑍 = πœŒπ‘
Physics data booklet
11
Sub-topic D.1 – Stellar quantities
𝑑 (parsec) =
𝐿 = πœŽπ΄π‘‡
𝑏=
4
1
𝑝 (arc–second)
𝐿
4πœ‹π‘‘ 2
Sub-topic D.3 – Cosmology
𝑧=
βˆ†πœ† 𝑣
≈
πœ†0 𝑐
𝑧=
𝑅
−1
𝑅0
𝑇≈
1
𝐻0
𝑣 = 𝐻0 𝑑
Physics data booklet
Sub-topic D.2 – Stellar characteristics and stellar
evolution
πœ†max 𝑇 = 2.9 × 10−3 m K
𝐿 ∝ 𝑀3.5
Sub-topic D.5 – Further cosmology (HL only)
4πœ‹πΊπœŒ
𝑣=οΏ½
π‘Ÿ
3
𝜌c =
3𝐻 2
8πœ‹πΊ
12
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