Regents Physics modern physics: a complete skills guide to the dual nature of light, the Bohr model and atomic spectra, mass-energy, nuclear physics and the Standard Model

Why modern physics ties the course together

Modern physics is where the quantities you have studied (energy, charge, mass, frequency) reappear at the scale of atoms and nuclei, and where the wave ideas from the previous module meet the particle picture. The calculations are short and rely on a few Reference-Table equations, while the concepts (duality, quantisation, mass-energy, the Standard Model) are tested in their own right. This guide ties together the dot-point pages, each with its own practice: the dual nature of light, the Bohr model and atomic spectra, mass-energy and nuclear physics and the Standard Model.

The dual nature of light

Light is both a wave (diffraction, interference) and a stream of photons (the photoelectric effect). A photon's energy is $E_{photon} = hf = \dfrac{hc}{\lambda}$, with $h = 6.63 \times 10^{-34}$ J s, so a higher frequency means a more energetic photon. The photoelectric effect, light ejecting electrons only above a threshold frequency, can be explained only by photons, not by waves. The duality is symmetric: matter has a wave nature, with de Broglie wavelength $\lambda = \dfrac{h}{mv}$, significant only for tiny, fast particles. Both equations are on the Reference Tables.

The Bohr model and atomic spectra

An atom's electrons occupy only quantised energy levels. An electron absorbs a photon to rise and emits one to drop, with the photon energy equal to the level difference: $E_{photon} = E_i - E_f$. Because only certain differences exist, atoms emit and absorb only certain wavelengths, giving each element a characteristic line spectrum. Energy levels are negative (relative to a free electron at zero); the hydrogen levels are listed on the Reference Tables' energy-level diagram. Careful sign handling is the main calculation skill.

Mass-energy and nuclear physics

Mass and energy are equivalent, $E = mc^2$, and because $c^2$ is enormous, a tiny mass yields a huge energy. A nucleus weighs less than its separate nucleons; the mass defect corresponds (via $E = mc^2$) to the binding energy holding it together. Fission (splitting heavy nuclei) and fusion (joining light nuclei) both release energy because the products have less total mass than the reactants. The Reference Tables print $E = mc^2$ and the conversion $1$ universal mass unit $= 931$ MeV; there is no half-life formula, so decay is reasoned from data.

The Standard Model

The Standard Model sorts fundamental matter into quarks and leptons. The six quarks carry fractional charges: up-type (up, charm, top) $+\tfrac{2}{3}e$, down-type (down, strange, bottom) $-\tfrac{1}{3}e$. The leptons are the electron, muon and tau (charge $-1e$) and their neutrinos (charge $0$). Protons and neutrons are composite: a proton is two up and one down ($+1e$), a neutron one up and two down ($0$). The fractional charges, read from the Standard Model chart on the Reference Tables, add to whole numbers in composite particles.

Check your knowledge

A mix of recall, calculation and reasoning questions covering the modern physics module. Attempt them under timed conditions, then check against the solutions.

1. State the energy of a photon in terms of its frequency. (1 mark)
2. A photon has a frequency of $4.0 \times 10^{14}$ Hz. Calculate its energy ($h = 6.63 \times 10^{-34}$ J s). (2 marks)
3. State what the photoelectric effect shows about light. (1 mark)
4. State why an atom emits only certain wavelengths of light. (2 marks)
5. An electron drops from a $-1.51$ eV level to a $-3.40$ eV level. Calculate the emitted photon's energy. (2 marks)
6. State the equation relating mass and energy. (1 mark)
7. A mass of $1.0 \times 10^{-3}$ kg is converted to energy. Calculate the energy released ($c = 3.00 \times 10^8$ m/s). (2 marks)
8. State what the mass defect of a nucleus is. (1 mark)
9. State the two families of fundamental particles in the Standard Model. (2 marks)
10. A proton is two up quarks ($+\tfrac{2}{3}e$) and one down quark ($-\tfrac{1}{3}e$). Calculate its charge. (2 marks)