Quick questions on Quantum model of light and the photoelectric effect: HSC Physics Module 7

By the late 1800s the wave model of light was the standard. But in 1887 Heinrich Hertz noticed UV light striking metal electrodes increased the spark distance in his radio-wave apparatus. Lenard's careful experiments (1902) revealed three features the wave model could not explain:

Building on Planck's 1900 idea that energy is exchanged in discrete amounts $h f$, Einstein proposed that light itself is made of discrete energy packets:

The minimum frequency that can eject any electron is the one where $KE_{\max} = 0$:

In the standard experiment, a positive collector electrode is gradually reverse-biased until the most energetic photoelectrons are turned back. The reversing voltage at which photocurrent vanishes is the stopping voltage $V_s$:

Caesium has work function $\phi = 2.10$ eV. Calculate the maximum kinetic energy and stopping voltage when light of wavelength $400$ nm illuminates the cathode.

Three predictions of the classical wave model are flatly contradicted:

$h = 6.626 \times 10^{-34}$ J s is the universal constant relating frequency to energy quantum. It also appears in:

The signs are: photon energy in, work function out, kinetic energy out. So $h f = \phi + KE_{\max}$.

Intensity sets the photon flux (number per second), so it sets the current, not the energy per electron.

Higher frequency = shorter wavelength = more energetic photon. Threshold frequency $f_0$ corresponds to maximum (cut-off) wavelength $\lambda_0 = c / f_0$.

It is the work function of the bulk metal: the energy needed to remove an electron from the metal surface to a stationary state just outside.

Each photon is absorbed entire by one electron in a single quantum event; there is no shaking.