Modern Physics

Notes

Quantum ideas

• Light comes in packets called photons, each with energy $\displaystyle E = hf = \frac{hc}{\lambda}$, where $h = 6.63 \times 10^{-34}$ J·s. Higher frequency (bluer) photons have more energy.
• Photoelectric effect: light shining on metal ejects electrons only if each photon has enough energy. $K_{max} = hf - \phi$, where $\phi$ is the work function. Brighter light (more photons) ejects more electrons but doesn't raise their maximum energy. This is evidence that light is a particle.
• Wave-particle duality: matter also has a wavelength, $\displaystyle \lambda = \frac{h}{p}$ (de Broglie). Electron diffraction shows electrons act like waves.

Atoms and spectra

• Electrons in atoms have discrete energy levels. Dropping from a higher to a lower level emits a photon with $E = E_{high} - E_{low}$; absorbing a photon of exactly that energy raises the electron.
• This gives each element a unique emission or absorption spectrum.

Nuclear physics

• The nucleus has protons and neutrons held by the strong nuclear force. Isotopes have the same protons but different neutrons.
• Alpha decay emits $^4_2\text{He}$ (mass number −4, atomic number −2). Beta-minus decay turns a neutron into a proton and emits an electron (atomic number +1). Gamma decay emits a high-energy photon (no change in particles).
• Nucleon number and charge are conserved in nuclear reactions.
• Half-life: the time for half of a radioactive sample to decay. After $n$ half-lives, $\displaystyle \left(\frac{1}{2}\right)^n$ remains.
• Mass-energy equivalence: $E = mc^2$. In fission and fusion, the products have slightly less mass; the mass defect becomes energy.