Modern physics is the physics of the very small: photons, electrons, atoms and nuclei. Around 1900 experiments began to turn up results that classical physics could not explain at all: light that knocks electrons out of a metal only above a certain frequency, atoms that give out sharp coloured lines instead of a smooth rainbow, and nuclei that throw out particles all by themselves. Explaining them led to the quantum idea, and the energy of nuclei was later understood through Einstein’s E = mc².
This module follows that story in three parts: the photoelectric effect and the photon, with the wave–particle duality it opened up; the structure of the atom, from Thomson’s and Rutherford’s models to Bohr’s energy levels and line spectra; and the nucleus, covering radioactivity, half-life, binding energy, fission and fusion.
The mathematics is light. Most questions come down to one equation (E_k = hν − W₀, hν = Eₘ − Eₙ, N = N₀(1/2)^(t/T) or ΔE = Δmc²) plus careful work with electronvolts. Learn the routine in each section and this becomes one of the most dependable parts of the paper.
Modern Physics is one of the five content modules in the official CSCA Physics syllabus, which names three topics: the photoelectric effect, atomic structure and the fundamentals of nuclear physics. The questions are single-answer multiple choice, and questions on these topics can take forms such as: applying E_k = hν − W₀ and reading photoelectric graphs; using an energy-level diagram to find photon energies, wavelengths and numbers of spectral lines; interpreting α-particle scattering; balancing decay and reaction equations; half-life calculations; and mass-defect, binding-energy, fission and fusion problems. Most need one equation and careful units, so they reward practice with electronvolts and atomic mass units.
Shine ultraviolet light on a clean zinc plate attached to a negatively charged electroscope and the leaves fall: the light knocks electrons out of the metal. This is the photoelectric effect (光电效应), and the electrons released are photoelectrons (光电子). In the laboratory it is studied with a phototube (光电管): light falls on a metal cathode K, the freed electrons cross a vacuum to an anode A, and a sensitive meter measures the photocurrent.
Classical wave theory fails on every point. A wave delivers energy continuously, so brighter light ought to give faster electrons, any frequency ought to work if you wait long enough, and dim light ought to need time to build up enough energy in an electron.
Einstein proposed that light consists of photons (光子), each carrying energy ε = hν = hc/λ, where h = 6.63 × 10⁻³⁴ J·s is the Planck constant. One photon gives all its energy to one electron. At least the work function W₀ (逸出功) is used up getting the electron out of the metal, and the rest becomes kinetic energy. For the electrons that escape most easily this gives the photoelectric equation (光电效应方程):
E_k = hν − W₀
The threshold follows at once: emission needs hν ≥ W₀, so ν_c = W₀/h and the threshold wavelength is λ_c = hc/W₀. Doubling the intensity doubles the number of photons, and so of electrons, but each photon still has the same energy, so E_k does not change. Work functions are a few electronvolts: about 2.25 eV for potassium and 3.34 eV for zinc.
Make the anode negative and the electrons must climb a potential hill. The current falls to zero at the stopping voltage U_c (遏止电压), when even the fastest electrons are turned back: eU_c = E_k = hν − W₀. So a stopping voltage of 1.5 V means a maximum kinetic energy of 1.5 eV. With a forward voltage the current rises until every emitted electron is collected, giving the saturation current (饱和电流). Light of one frequency but different intensities gives I–U curves with different saturation currents but the same stopping voltage; light of a higher frequency gives a larger stopping voltage.
Two metals give two parallel lines; the one further to the right has the larger work function.
Atomic energies are measured in electronvolts: 1 eV = 1.6 × 10⁻¹⁹ J. A handy shortcut is hc = 6.63 × 10⁻³⁴ × 3.0 × 10⁸ ≈ 1.99 × 10⁻²⁵ J·m ≈ 1240 eV·nm, so a photon of wavelength λ (in nm) has energy 1240/λ eV: 400 nm violet light carries about 3.1 eV and 700 nm red light about 1.8 eV.
💡Light comes in photons of energy hν. One photon frees one electron: E_k = hν − W₀, the threshold is ν_c = W₀/h, and eU_c = E_k. Frequency sets the electrons’ energy; intensity sets how many there are.
📋 Key Formulas
📝 Worked Example 1
Example 1: Light of wavelength 300 nm falls on potassium (W₀ = 2.25 eV). Find the maximum kinetic energy of the photoelectrons and the stopping voltage.
Step 1: Photon energy: hc/λ = (6.63 × 10⁻³⁴ × 3.0 × 10⁸)/(3.0 × 10⁻⁷) = 6.63 × 10⁻¹⁹ J, and 6.63 × 10⁻¹⁹/1.6 × 10⁻¹⁹ ≈ 4.14 eV.
Step 2: E_k = hν − W₀ = 4.14 − 2.25 = 1.89 eV (about 3.0 × 10⁻¹⁹ J).
Step 3: eU_c = E_k, so U_c = 1.89 V. Working in electronvolts makes this step immediate.
📝 Worked Example 2
Example 2: The work function of zinc is 3.34 eV. Can visible light (400–700 nm) eject electrons from zinc?
Step 1: W₀ = 3.34 × 1.6 × 10⁻¹⁹ = 5.34 × 10⁻¹⁹ J, so ν_c = W₀/h = 5.34 × 10⁻¹⁹/6.63 × 10⁻³⁴ ≈ 8.1 × 10¹⁴ Hz.
Step 2: λ_c = c/ν_c = 3.0 × 10⁸/8.1 × 10¹⁴ ≈ 3.7 × 10⁻⁷ m = 370 nm.
Step 3: Visible light has λ > 400 nm, longer than λ_c, so each photon carries too little energy: no. Zinc needs ultraviolet, however bright the visible light is.
📝 Worked Example 3
Example 3: The E_k–ν graph for a metal is a straight line cutting the ν-axis at 5.0 × 10¹⁴ Hz. Find the work function, and E_k for light of 7.5 × 10¹⁴ Hz.
Step 1: The intercept is the threshold frequency, so W₀ = hν_c = 6.63 × 10⁻³⁴ × 5.0 × 10¹⁴ ≈ 3.3 × 10⁻¹⁹ J ≈ 2.1 eV.
Step 2: E_k = h(ν − ν_c) = 6.63 × 10⁻³⁴ × 2.5 × 10¹⁴ ≈ 1.7 × 10⁻¹⁹ J (about 1.0 eV).
🧠Convert between eV and J with 1 eV = 1.6 × 10⁻¹⁹ J, or use hc ≈ 1240 eV·nm to get photon energies straight in electronvolts.
🧠Brighter light means more photoelectrons (a bigger saturation current), never faster ones; only a higher frequency raises E_k and U_c.
🧠On an E_k–ν or U_c–ν graph the ν-intercept is the threshold frequency; on the E_k–ν graph the gradient is h for every metal.
⚠️Thinking intensity raises the electron energy: intensity changes the number of photons, not the energy of each one.
⚠️Using W₀ in eV and hν in J in the same equation: put everything in one unit before subtracting.
⚠️Confusing the stopping voltage with the work function: eU_c is the maximum kinetic energy, hν − W₀, not W₀ itself.
🎯 Try This Yourself
Light of frequency 1.0 × 10¹⁵ Hz falls on a metal whose work function is 2.5 eV. Find the stopping voltage.
You have finished Modern Physics. You can now use the photon model to explain the photoelectric effect, calculate maximum kinetic energies, threshold frequencies and stopping voltages, and describe light and matter as having both wave and particle properties. You can explain how α-particle scattering revealed the nucleus, use Bohr’s energy levels to find photon energies, wavelengths and numbers of spectral lines, and tell emission and absorption spectra apart. In nuclear physics you can balance decay and reaction equations, solve half-life problems, and calculate mass defects, binding energies and the energy released in fission and fusion.
The habit that ties it all together: work in electronvolts, find the energy difference or the change in mass, and always check that mass number and charge number balance.
Open and read all sections to complete this module