OPOpenPithMake curiosity visiblePhysics lab / Modern physics

About this lab

Six experiments, two discoveries: light comes in lumps, and so do atoms.

The first three experiments are about the photoelectric effect: whether light frees electrons from a metal, and how much energy they carry, depend only on its frequency. Only photons explain this: each lump of light carries hν. The last three are about atoms: alpha scattering reveals a tiny nucleus, and the hydrogen spectrum and the Franck–Hertz experiment show that an atom’s energy takes only certain values.

Every reading, dot and curve comes from the same physical model, not a pre-drawn animation. Change one parameter and all the data is recalculated together.

Six conclusions

Each experiment overturns a common idea.

Bright enough light always frees electrons?

An ultraviolet photon carries 4.88 eV, more than zinc’s work function of 3.34 eV, so the negative plate soon discharges; a red photon has only 1.91 eV, and even triple the brightness frees nothing. Frequency decides whether electrons escape; intensity only decides how fast.

Brighter light, more energetic electrons?

With 405 nm light on sodium, doubling the power from 10 µW to 20 µW leaves the stopping voltage at 0.77 V while the saturation current rises from 32.6 nA to 65.3 nA. Intensity sets how many electrons there are, not their maximum energy.

A new metal, a new slope?

Three mercury lines that free electrons from sodium give a Uc–ν slope of h = 6.63 × 10⁻³⁴ J·s; with rubidium the line shifts but keeps the same slope.

Alpha particles can never bounce back?

The Thomson model predicts almost no counts beyond 10°; the gold foil still gives 19 flashes in 5 minutes at 150°. The atom’s positive charge and nearly all its mass sit in a tiny nucleus.

Hydrogen light is a continuous rainbow?

The hydrogen tube gives just four visible lines, red Hα at 23.2°; fitting the grating readings gives R = 1.0967 × 10⁷ m⁻¹. Separate lines mean separate energy levels.

Atoms absorb any amount of energy?

The anode current in the mercury tube does not simply rise; it drops at regular steps, with a spacing of 4.9 V, which is mercury’s first excitation energy and matches its 254 nm ultraviolet line.

Model and sources

Model and sources

  • Photoelectric effect: Ek,max = hν − W₀, eUc = Ek,max; saturation current Is = ηeP/(hν), quantum efficiency η = 1%.
  • Alpha scattering: counts at a fixed detector N ∝ 1/sin⁴(θ/2); counts are Poisson samples with a fixed seed.
  • Hydrogen: 1/λ = R(1/2² − 1/n²), R_H = R∞/(1 + mₑ/mₚ); grating 600 lines/mm, d sinθ = λ, read to 1′.
  • Franck–Hertz: spacing of the current dips = E₁/e; mercury 4.9 eV, neon 18.9 eV, the middle of its 18.3–19.5 eV levels.
  • Constants are the SI defined values: h = 6.62607015 × 10⁻³⁴ J·s, e = 1.602176634 × 10⁻¹⁹ C, c = 299792458 m/s.

Work functions are textbook table values (zinc 3.34 eV, sodium 2.29 eV, rubidium 2.13 eV, calcium 3.20 eV); handbooks give about 4.3 eV for clean zinc, and the surface makes a large difference. The quantum efficiency, the shape of the I–U curve, glass stopping ultraviolet below 320 nm, the alpha count scale (about 3 per minute at 150°), the Thomson model’s 1° deflection and the shape and contact offset of the Franck–Hertz curve are teaching assumptions: they shape the curves and counts, not the stopping voltages, h, line positions or dip spacing. Mercury lines are air wavelengths and hydrogen lines vacuum wavelengths; they differ by about 0.03%. Bohr orbits are a historical model; the level diagram shows energies, not electron paths.

Back to physics ↑