Photon

A particle representing a quantum of light.

Quantum

Smallest discrete amount of something.

Discrete

An individually separate and distinct thing. Not made of anything else.

Photons exhibit wave properties under refraction and interference.

Photons exhibit particle properties under emission or absorption.

$E = hf = \frac{hc}{\lambda}$

Where h is Planck's constant, c is the speed of light, and λ is its wavelength.

Threshold Frequency

The minimum frequency for the emission of electrons due to incident radiation.

Work Function

The minimum quantity of energy required to remove an electron from a solid.

Stopping Potential

The minimum negative voltage applied to the anode to stop the photocurrent, representing the maximum kinetic energy of the electron.

$\Phi = hf_0$, where $f_0$ is the threshold frequency.

Total energy: $hf = \Phi + E_k$

Threshold wavelength: $\lambda_c = \frac{hc}{\Phi}$

De Broglie proposed that all matter has wave-like properties.

Momentum-wavelength relation: $p = \frac{h}{\lambda}$

Electrons orbit the nucleus in discrete paths with quantized angular momentum.

Nuclear radius: $R = R_0 A^{\frac{1}{3}}$

Energy levels: $E_n = -R_H \left(\frac{1}{n^2}\right)$

Angular momentum: $mvr = \frac{nh}{2\pi}$

Energy of an electron in orbit: $E = -\left(\frac{13.6}{n^2}\right) eV$

Rutherford's students shot alpha particles at gold foil.

The Plum Pudding Model predicted uniform density, meaning no deflection, but scattering was observed, proving the nuclear model of the atom.

The nucleus moves between discrete energy levels, often emitting gamma rays corresponding to distinct energy transitions.

Electrons moving down in energy levels emit photons, forming an emission spectrum.

Absorption spectra show wavelengths absorbed as electrons move up energy levels.

Arthur Compton observed an increase in photon wavelength after colliding with an electron, leading to a wavelength shift formula:

$\Delta \lambda = \frac{h}{m_e c} (1 - \cos \theta)$

The energy used to accelerate electrons equals their kinetic energy.

$\lambda = \frac{h}{\sqrt{2mqV}}$