Key ideas
Modern physics describes light and matter at small scales. Light comes in quanta called photons, particles have wavelengths, atoms have discrete energy levels, and nuclei decay at random with fixed half-lives.
- A photon has energy E = hf = hc ÷ λ. With hc = 1240 eV·nm, a wavelength in nanometers gives the energy in electronvolts directly.
- In the photoelectric effect K_max = hf − φ. Frequency decides whether electrons come out; intensity only decides how many.
- A particle of momentum p has de Broglie wavelength λ = h ÷ p. Hydrogen levels are E_n = −13.6 eV ÷ n², and light is emitted when an electron falls between levels.
- After each half-life, half of the remaining nuclei decay: N = N₀(½)^(t ÷ T½). Mass and energy are linked by E = mc².
Key equations
E = hf = hc ÷ λK_max = hf − φλ = h ÷ pE_n = −13.6 eV ÷ n²N = N₀(½)^(t ÷ T½)E = mc²
Worked example
Ultraviolet light of wavelength 200 nm falls on a metal with work function 4.0 eV. The photon energy is 1240 ÷ 200 = 6.2 eV. The maximum kinetic energy of the emitted electrons is 6.2 − 4.0 = 2.2 eV. Red light of 700 nm has only 1.8 eV and cannot free any electron, however intense it is.
Common mistakes
- Thinking brighter light gives faster electrons. Brighter light gives more electrons; faster ones need higher frequency.
- Mixing joules and electronvolts, or using wavelength in meters with the value of hc in eV·nm.
- Believing that a sample is gone after two half-lives. A quarter is still left.
Practice
Test yourself with practice questions on this topic: Modern physics