IB Physics Data Booklet Reference

How to Use This Guide

The IB Physics Data Booklet is your official formula sheet for all exams — Paper 1, Paper 2, and Paper 3. This guide helps you:

• Understand what’s given — constants, equations, and tables you can reference during exams
• Know what to memorize — core concepts and relationships NOT in the booklet
• Navigate efficiently — find formulas quickly under exam pressure
• Avoid common mistakes — unit errors, sign conventions, and factor-of-2 pitfalls

This guide is based on the IB Physics Data Booklet for first assessment 2025+. Always verify with your teacher that you have the current version.

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Jump to section: Fundamental Constants · Unit Prefixes & Conversions · Theme A: Motion · Theme B: Particulate Nature · Theme C: Waves · Theme D: Fields · Theme E: Nuclear & Quantum · Exam Strategies

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Section 1: Fundamental Constants

These constants appear throughout physics calculations. The Data Booklet provides precise values — you don’t need to memorize them.

Universal Constants

Symbol	Constant	Value (from booklet)	Units
$c$	Speed of light in vacuum	$3.00 \times 10^8$	$\text{m s}^{-1}$
$G$	Gravitational constant	$6.67 \times 10^{-11}$	$\text{N m}^2 \text{ kg}^{-2}$
$N_A$	Avogadro constant	$6.02 \times 10^{23}$	$\text{mol}^{-1}$
$R$	Molar gas constant	$8.31$	$\text{J K}^{-1} \text{ mol}^{-1}$
$k_B$	Boltzmann constant	$1.38 \times 10^{-23}$	$\text{J K}^{-1}$
$\sigma$	Stefan-Boltzmann constant	$5.67 \times 10^{-8}$	$\text{W m}^{-2} \text{ K}^{-4}$

Electromagnetic Constants

Symbol	Constant	Value (from booklet)	Units
$e$	Elementary charge	$1.60 \times 10^{-19}$	$\text{C}$
$\epsilon_0$	Permittivity of free space	$8.85 \times 10^{-12}$	$\text{F m}^{-1}$
$\mu_0$	Permeability of free space	$4\pi \times 10^{-7}$	$\text{H m}^{-1}$
$h$	Planck constant	$6.63 \times 10^{-34}$	$\text{J s}$

Particle Masses

Particle	Symbol	Mass (from booklet)	Units
Electron	$m_e$	$9.11 \times 10^{-31}$	$\text{kg}$
Proton	$m_p$	$1.673 \times 10^{-27}$	$\text{kg}$
Neutron	$m_n$	$1.675 \times 10^{-27}$	$\text{kg}$
Unified atomic mass unit	$u$	$1.661 \times 10^{-27}$	$\text{kg}$

Earth and Astronomical Data

The booklet includes:

• Mass of Earth: $M_E = 5.97 \times 10^{24}$ kg
• Mean radius of Earth: $R_E = 6.37 \times 10^6$ m
• Gravitational field strength at Earth’s surface: $g = 9.81$ m s$^{-2}$
• Mass of Sun: $M_S = 1.99 \times 10^{30}$ kg
• Mean Earth-Sun distance: $1.50 \times 10^{11}$ m (1 AU)

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Section 2: Unit Prefixes and Conversions

Metric Prefixes (Given in Booklet)

Prefix	Symbol	Factor	Example
tera	T	$10^{12}$	1 TW = $10^{12}$ W
giga	G	$10^9$	1 GHz = $10^9$ Hz
mega	M	$10^6$	1 MeV = $10^6$ eV
kilo	k	$10^3$	1 km = $10^3$ m
centi	c	$10^{-2}$	1 cm = $10^{-2}$ m
milli	m	$10^{-3}$	1 ms = $10^{-3}$ s
micro	$\mu$	$10^{-6}$	1 $\mu$F = $10^{-6}$ F
nano	n	$10^{-9}$	1 nm = $10^{-9}$ m
pico	p	$10^{-12}$	1 pF = $10^{-12}$ F
femto	f	$10^{-15}$	1 fm = $10^{-15}$ m

Common Unit Conversions

The booklet provides:

• 1 electronvolt (eV) = $1.60 \times 10^{-19}$ J
• 1 day = $8.64 \times 10^4$ s
• 1 year = $3.16 \times 10^7$ s
• 1 light year (ly) = $9.46 \times 10^{15}$ m
• 1 parsec (pc) = $3.08 \times 10^{16}$ m

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Section 3: Theme A — Space, Time and Motion

Given in the Booklet (All Levels)

Kinematics:

• $v = u + at$ (constant acceleration)
• $s = ut + \frac{1}{2}at^2$
• $v^2 = u^2 + 2as$
• $s = \frac{1}{2}(u+v)t$

Projectile motion:

• Horizontal: $x = v_x t$
• Vertical: $y = v_y t - \frac{1}{2}gt^2$

Momentum and collisions:

• $p = mv$ (momentum)
• $F = \frac{\Delta p}{\Delta t}$ (Newton’s second law, impulse form)

Energy and work:

• $E_k = \frac{1}{2}mv^2$ (kinetic energy)
• $E_p = mgh$ (gravitational potential energy near Earth’s surface)
• $W = Fs\cos\theta$ (work done)
• $P = \frac{W}{t}$ (power)
• Efficiency: $\eta = \frac{\text{useful energy output}}{\text{total energy input}}$

Circular motion:

• $v = \frac{2\pi r}{T}$ (tangential speed)
• $a_c = \frac{v^2}{r}$ (centripetal acceleration)
• $F_c = \frac{mv^2}{r}$ (centripetal force)

NOT Given (Must Memorize)

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Section 4: Theme B — The Particulate Nature of Matter

Given in the Booklet (All Levels)

Thermal physics:

• $pV = nRT$ (ideal gas law)
• $E_k = \frac{3}{2}kT$ (mean kinetic energy of ideal gas molecule)
• $Q = mc\Delta T$ (heat energy transfer, specific heat)
• $Q = mL$ (latent heat)

Internal energy and thermodynamics:

• First law: $\Delta U = Q - W$
• $W = p\Delta V$ (work done by gas at constant pressure)

Density and pressure:

• $\rho = \frac{m}{V}$ (density)
• $p = \frac{F}{A}$ (pressure)

Given in the Booklet (HL Only) HL

• $pV^\gamma = \text{constant}$ (adiabatic process)
• Carnot efficiency: $\eta = 1 - \frac{T_C}{T_H}$
• Entropy change: $\Delta S = \frac{Q}{T}$ (reversible process)

NOT Given (Must Memorize)

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Section 5: Theme C — Wave Behaviour

Given in the Booklet (All Levels)

Wave properties:

• $v = f\lambda$ (wave equation)
• $f = \frac{1}{T}$ (frequency and period)

Electromagnetic spectrum:

• The booklet includes a table showing wavelength ranges for radio, microwave, infrared, visible, UV, X-ray, gamma

Optics:

• $n = \frac{c}{v}$ (refractive index)
• Snell’s law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$
• Critical angle: $\sin\theta_c = \frac{n_2}{n_1}$ (for $n_1 > n_2$)
• Lens equation: $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$
• Magnification: $m = \frac{v}{u}$

Interference:

• Double-slit: $d\sin\theta = n\lambda$ (maxima)
• Single-slit diffraction: $b\sin\theta = n\lambda$ (minima)

Doppler effect:

• For sound: $f' = f \frac{v \pm v_o}{v \mp v_s}$
• For light (non-relativistic): $\frac{\Delta f}{f} = \frac{v}{c}$ (approaching source)

Given in the Booklet (HL Only) HL

• Diffraction grating: $d\sin\theta = n\lambda$
• Rayleigh criterion: $\theta \approx 1.22\frac{\lambda}{b}$
• Relativistic Doppler: $f' = f\sqrt{\frac{1+v/c}{1-v/c}}$

NOT Given (Must Memorize)

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Section 6: Theme D — Fields

Given in the Booklet (All Levels)

Gravitational fields:

• $g = \frac{F}{m}$ (field strength)
• $F = \frac{Gm_1m_2}{r^2}$ (Newton’s law of gravitation)
• $g = \frac{GM}{r^2}$ (field strength at distance $r$)
• $V = -\frac{GM}{r}$ (gravitational potential)
• $E_p = -\frac{GMm}{r}$ (gravitational potential energy)

Orbital motion:

• $v = \sqrt{\frac{GM}{r}}$ (orbital speed)
• $T^2 = \frac{4\pi^2}{GM}r^3$ (Kepler’s third law)

Electric fields:

• $F = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}$ (Coulomb’s law, also written as $F = k\frac{q_1q_2}{r^2}$ where $k = \frac{1}{4\pi\epsilon_0}$)
• $E = \frac{F}{q}$ (electric field strength)
• $E = \frac{V}{d}$ (uniform field between plates)
• $V = \frac{Q}{4\pi\epsilon_0 r}$ (electric potential, point charge)
• $C = \frac{Q}{V}$ (capacitance)
• $E = \frac{1}{2}QV = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C}$ (energy stored in capacitor)

Magnetic fields:

• $F = BIl\sin\theta$ (force on current-carrying wire)
• $F = Bqv\sin\theta$ (force on moving charge)

Given in the Booklet (HL Only) HL

• $r = \frac{mv}{Bq}$ (radius of circular path in magnetic field)
• Faraday’s law: $\mathcal{E} = -N\frac{\Delta\Phi}{\Delta t}$
• Magnetic flux: $\Phi = BA\cos\theta$
• $\mathcal{E} = Blv$ (motional EMF)

NOT Given (Must Memorize)

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Section 7: Theme E — Nuclear and Quantum Physics

Given in the Booklet (All Levels)

Photon energy and quantum theory:

• $E = hf$ (photon energy)
• $E = \frac{hc}{\lambda}$ (alternative form)
• $E_k = hf - \phi$ (photoelectric effect)
• $\lambda = \frac{h}{p}$ (de Broglie wavelength)

Nuclear physics:

• $E = mc^2$ (mass-energy equivalence)
• $A = \lambda N$ (radioactive decay activity)
• $N = N_0 e^{-\lambda t}$ (exponential decay law)
• $T_{1/2} = \frac{\ln 2}{\lambda}$ (half-life)

Atomic structure:

• $\frac{1}{\lambda} = R\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$ (Rydberg formula for hydrogen spectrum)
• Rydberg constant: $R = 1.097 \times 10^7$ m$^{-1}$

Given in the Booklet (HL Only) HL

• Schrödinger equation (time-independent): $-\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + V\psi = E\psi$
• Heisenberg uncertainty principle: $\Delta x \Delta p \geq \frac{\hbar}{2}$ (where $\hbar = h/2\pi$)
• Tunneling probability expressions

NOT Given (Must Memorize)

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Section 8: Exam Strategies for Using the Data Booklet

1. Know the Layout

The Data Booklet is organized by theme (A, B, C, D, E). Spend 5 minutes at the start of your course familiarizing yourself with the booklet’s structure:

• Page 1: Constants and conversion factors
• Pages 2-6: Formulae organized by theme (A through E)
• Page 7: Standard model of particle physics (HL)
• Page 8: Electromagnetic spectrum, units, SI prefixes

2. Understand vs. Locate

Don’t treat the Data Booklet as a crutch. You still need to:

• Understand when to use each formula (the booklet doesn’t tell you which equation applies to which problem)
• Know variable meanings (is $r$ radius, distance, or separation?)
• Recognize units (does your answer need to be in eV or Joules?)

3. Memorize Strategic Shortcuts

While most formulas are given, memorizing a few relationships saves time:

4. Check Units and Factors

Many formulas have factors like $\frac{1}{2}$, $2\pi$, or $4\pi$. Common mistakes:

Formula	Common Error	Correct Form
$E_k = \frac{1}{2}mv^2$	Forgetting $\frac{1}{2}$	Always include the half
$v = \frac{2\pi r}{T}$	Writing $v = \frac{r}{T}$	Don’t drop $2\pi$
Coulomb’s law	Forgetting $4\pi\epsilon_0$	$F = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}$
Half-life	Using $\lambda$ instead of $\ln 2$	$T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$

5. Cross-Reference Related Formulas

Some physics problems require combining multiple equations. The Data Booklet doesn’t show derivations, so practice connecting formulas:

Example: To find escape velocity from a planet, you combine:

• Gravitational potential energy: $E_p = -\frac{GMm}{r}$
• Kinetic energy: $E_k = \frac{1}{2}mv^2$
• Conservation of energy: $E_k + E_p = 0$ at infinity

Result (NOT in booklet): $v_{\text{esc}} = \sqrt{\frac{2GM}{r}}$

6. Flag HL-Only Content

If you’re taking SL, ignore formulas marked “HL only” in the booklet (they appear in a separate section or are marked explicitly). Spending time on irrelevant equations wastes exam minutes.

7. Practice Under Exam Conditions

In mock exams:

1. Time yourself — can you find a formula in under 10 seconds?
2. Mark up the booklet — you’re allowed to write in it during the exam (though it’s discarded after). Use it to track which page has which theme.
3. Check the version — ensure you’re practicing with the 2025+ booklet, not an outdated version.

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Exam-Style Practice Questions

Question 1: A student claims they don’t need to memorize any physics formulas because “it’s all in the Data Booklet.” Evaluate this claim. [4 marks]

Answer:

The claim is partially correct but demonstrates a misunderstanding of how the Data Booklet is used. [1 mark for acknowledging partial truth]

What the booklet provides:

• The booklet contains most formulas (kinematics, energy, fields, quantum) and all fundamental constants. [1 mark]

What the booklet does NOT provide:

• Conceptual understanding of when to use each formula [1 mark]
• Derivations linking multiple equations (e.g., escape velocity, orbital mechanics combined with energy conservation)
• Core definitions (e.g., Newton’s laws stated in words, conservation principles, wave properties)

Conclusion: Students must memorize core physics concepts, understand variable meanings, and practice applying formulas in context. The booklet is a reference, not a substitute for understanding. [1 mark for clear conclusion]

Question 2: The Data Booklet gives gravitational potential energy as $E_p = -\frac{GMm}{r}$ but many textbooks use $E_p = mgh$ near Earth’s surface. Explain why both are correct and state when each should be used. [3 marks]

Answer:

Both formulas describe gravitational potential energy but apply in different contexts:

1. $E_p = -\frac{GMm}{r}$ is the general formula for gravitational potential energy at distance $r$ from a point mass $M$. The negative sign indicates energy is zero at infinity and becomes more negative closer to the mass. [1 mark]

2. $E_p = mgh$ is an approximation valid near Earth’s surface where $g$ is approximately constant ($9.81$ m s$^{-2}$). Here, $h$ is height above a reference level (often ground level), and we set $E_p = 0$ at that reference. [1 mark]

When to use each:

• Use $E_p = mgh$ for objects near Earth’s surface (heights up to a few km where $g$ is roughly constant).
• Use $E_p = -GMm/r$ for satellites, orbital mechanics, or when distance from Earth’s center changes significantly. [1 mark]

Note: The full formula can be approximated: for small $h$, $E_p = -\frac{GMm}{R_E + h} \approx -\frac{GMm}{R_E} + mgh$ where $g = GM/R_E^2$.

Question 3: A student finds three different formulas for capacitor energy in the Data Booklet: $E = \frac{1}{2}QV$, $E = \frac{1}{2}CV^2$, and $E = \frac{1}{2}\frac{Q^2}{C}$. Show that these are equivalent starting from $C = Q/V$. [3 marks]

Answer:

Starting point: $C = \frac{Q}{V}$ (definition of capacitance)

Derivation:

1. Energy stored in a capacitor is $E = \frac{1}{2}QV$ (this is the fundamental form derived from integrating $V$ dq). [Given]

2. From $C = Q/V$, we have $Q = CV$. Substituting into $E = \frac{1}{2}QV$: $E = \frac{1}{2}(CV)V = \frac{1}{2}CV^2$ [1 mark]

3. Alternatively, from $C = Q/V$, we have $V = Q/C$. Substituting into $E = \frac{1}{2}QV$: $E = \frac{1}{2}Q\left(\frac{Q}{C}\right) = \frac{1}{2}\frac{Q^2}{C}$ [1 mark]

Conclusion: All three formulas are mathematically equivalent. Use $E = \frac{1}{2}CV^2$ when voltage is known, $E = \frac{1}{2}Q^2/C$ when charge is known, and $E = \frac{1}{2}QV$ when both are known. [1 mark]

Question 4: The Data Booklet provides the formula $\lambda = h/p$ for de Broglie wavelength. A proton is accelerated through a potential difference of 100 V. Calculate its de Broglie wavelength. (Mass of proton $m_p = 1.673 \times 10^{-27}$ kg, $h = 6.63 \times 10^{-34}$ J s, $e = 1.60 \times 10^{-19}$ C) [4 marks]

Answer:

Step 1: Find kinetic energy gained by proton. When a proton (charge $e$) is accelerated through potential difference $V = 100$ V: $E_k = eV = (1.60 \times 10^{-19})(100) = 1.60 \times 10^{-17} \text{ J}$ [1 mark]

Step 2: Find momentum from kinetic energy. $E_k = \frac{1}{2}mv^2 = \frac{(mv)^2}{2m} = \frac{p^2}{2m}$ $p = \sqrt{2mE_k} = \sqrt{2(1.673 \times 10^{-27})(1.60 \times 10^{-17})}$ [1 mark] $p = \sqrt{5.35 \times 10^{-44}} = 2.31 \times 10^{-22} \text{ kg m s}^{-1}$ [1 mark]

Step 3: Calculate de Broglie wavelength. $\lambda = \frac{h}{p} = \frac{6.63 \times 10^{-34}}{2.31 \times 10^{-22}} = 2.87 \times 10^{-12} \text{ m} = 2.87 \text{ pm}$ [1 mark]

Answer: $\lambda = 2.87 \times 10^{-12}$ m (or 2.87 pm, comparable to atomic spacing in solids)

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Final Checklist for Data Booklet Mastery

Before your IB Physics exam, ensure you can:

• Locate any formula in the booklet within 10 seconds
• State from memory which formulas are NOT in the booklet (e.g., $F = ma$ standard form, conservation laws as concepts)
• Explain when to use general formulas vs. special cases (e.g., $E_p = -GMm/r$ vs. $E_p = mgh$)
• Identify all variables in context (e.g., distinguish orbital radius from planetary radius)
• Derive 5+ important relationships not directly given (escape velocity, Kepler’s third law proof, capacitor energy forms)
• Check units after every calculation
• Recognize common factor errors ($\frac{1}{2}$, $2\pi$, $4\pi\epsilon_0$)

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Related Guides:

• Space, Time and Motion — Theme A formulas in context
• Fields — Theme D formulas in context
• Nuclear and Quantum Physics — Theme E formulas in context
• Wave Behaviour — Theme C formulas in context
• Particulate Nature of Matter — Theme B formulas in context