Photons: the photon as a quantum of electromagnetic energy E = hf, the photoelectric effect and Einstein's equation, the work function and threshold frequency, and the electronvolt.

Photon energy: $E = \dfrac{hc}{\lambda} = \dfrac{(6.63 \times 10^{-34})(3.0 \times 10^{8})}{400 \times 10^{-9}} = \dfrac{1.989 \times 10^{-25}}{4.0 \times 10^{-7}} = 4.97 \times 10^{-19}\ \text{J}$.

Work function in joules: $\phi = 2.3 \times 1.6 \times 10^{-19} = 3.68 \times 10^{-19}\ \text{J}$.

Einstein's equation $hf = \phi + KE_\text{max}$: $KE_\text{max} = E - \phi = 4.97 \times 10^{-19} - 3.68 \times 10^{-19} = 1.3 \times 10^{-19}\ \text{J}$.

Markers reward the photon energy from $\frac{hc}{\lambda}$, converting the work function to joules, and $KE_\text{max} \approx 1.3 \times 10^{-19}\ \text{J}$.

Each photon carries a single quantum of energy $E = hf$, and one photon is absorbed by one electron. An electron can only escape if its photon supplies at least the work function $\phi$, so emission needs $hf \geq \phi$, i.e. a frequency at or above the threshold $f_0 = \frac{\phi}{h}$.

Below the threshold each photon has too little energy to free an electron, and increasing the intensity simply sends more such photons, none of which individually has enough energy: still no emission. The wave model wrongly predicts that enough intensity, given time, would always free electrons. The existence of a threshold frequency therefore supports the photon (quantum) model. Markers reward the one-photon-one-electron idea, the $hf \geq \phi$ condition, and explaining why intensity cannot compensate below the threshold.