AP PHYSICS 2 — physicsMedium3 min read

Quantum, Atomic & Nuclear Physics

AP Physics 2 review of quantum physics, the photoelectric effect, atomic models, energy levels, nuclear physics, and radioactive decay.

Tutor AI Team2026-02-26T00:11:18.357Z

# Quantum, Atomic & Nuclear Physics — AP Physics 2

Modern physics revolutionized our understanding of nature at the atomic and subatomic level. AP Physics 2 covers the photoelectric effect, wave-particle duality, atomic energy levels, nuclear structure, and radioactive decay.

Key Concepts

The Photoelectric Effect

Light ejects electrons from a metal surface. $E_{\text{photon}} = hf = \frac{hc}{\lambda}$ where $h = 6.63 \times 10^{-34}\ \text{J·s}$ .

$KE_{\max} = hf - \phi$ where $\phi$ is the work function (minimum energy to eject an electron).

Below the threshold frequency ( $f_0 = \phi/h$ ), no electrons are emitted regardless of intensity.
Increasing intensity increases the number of electrons, not their maximum KE.

Wave-Particle Duality

Light behaves as both a wave and a particle (photon).
de Broglie wavelength of a particle: $\lambda = h/p = h/(mv)$ .

Atomic Models

Bohr Model (Hydrogen):

Electrons occupy discrete energy levels.
Energy levels: $E_n = -\frac{13.6\ \text{eV}}{n^2}$
Photon emitted/absorbed when electron transitions: $E_{\text{photon}} = |E_f - E_i|$

Emission and Absorption Spectra

Emission spectrum: bright lines on dark background (excited atoms emit specific wavelengths).
Absorption spectrum: dark lines on continuous background (atoms absorb specific wavelengths).

Nuclear Structure

Atomic number ( $Z$ ): number of protons.
Mass number ( $A$ ): protons + neutrons.
Isotopes: same $Z$ , different $A$ .

Nuclear Reactions and Conservation Laws

Conservation of: charge, nucleon number (baryon number), energy, momentum.

Radioactive Decay

Type	Particle	$Z$ Change	$A$ Change
Alpha ( $\alpha$ )	$^4_2\text{He}$	$-2$	$-4$
Beta minus ( $\beta^-$ )	$e^-$	$+1$	$0$
Beta plus ( $\beta^+$ )	$e^+$	$-1$	$0$
Gamma ( $\gamma$ )	photon	$0$	$0$

Half-Life

$N = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}$

Mass-Energy Equivalence

$E = mc^2$

Mass defect: the mass of a nucleus is less than the sum of its parts. The "missing" mass is the binding energy.

Worked Example

Problem: UV light with wavelength $200\ \text{nm}$ strikes a metal with work function $\phi = 4.0\ \text{eV}$ . What is the maximum kinetic energy of the ejected electrons?

Solution:

$E_{\text{photon}} = hc/\lambda = (6.63 \times 10^{-34})(3 \times 10^8)/(200 \times 10^{-9}) = 9.945 \times 10^{-19}\ \text{J}$

Convert to eV: $9.945 \times 10^{-19} / 1.6 \times 10^{-19} = 6.22\ \text{eV}$

$KE_{\max} = 6.22 - 4.0 = 2.22\ \text{eV}$

Practice Questions

1. What is the energy of a photon with frequency $5 \times 10^{14}\ \text{Hz}$ ?

$E = hf = (6.63 \times 10^{-34})(5 \times 10^{14}) = 3.315 \times 10^{-19}\ \text{J} \approx 2.07\ \text{eV}$ .

2. An electron in hydrogen transitions from $n = 3$ to $n = 1$ . What is the photon energy?

$E = |E_1 - E_3| = |-13.6 - (-1.51)| = 12.09\ \text{eV}$ .

3. Uranium-238 undergoes alpha decay. Write the reaction and identify the daughter nucleus.

$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}$ . Daughter: Thorium-234.

4. A sample has a half-life of $10\ \text{days}$ . After $30\ \text{days}$ , what fraction remains?

$(1/2)^{30/10} = (1/2)^3 = 1/8$ .

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Summary

Photoelectric effect: $KE_{\max} = hf - \phi$ ; threshold frequency exists.
Bohr model: discrete energy levels, $E_n = -13.6/n^2$ eV for hydrogen.
Nuclear decay conserves charge and nucleon number; half-life governs decay rate.
$E = mc^2$ connects mass and energy; mass defect gives binding energy.

Tags:

#ap#physics#modern-physics

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