The Photoelectric Effect

In this faded example based on Problem 2.8, we apply the conservation of energy to the photoelectric effect. Electromagnetic radiation of $\lambda = 300 \text{ nm}$ falls on sodium, emitting electrons with a kinetic energy of $1.68 \times 10^5 \text{ J mol}^{-1}$. First, calculate the energy of a single 300 nm photon using $E = hc/\lambda$, which gives J. Next, find the energy of one mole of these photons by multiplying by Avogadro's number ($6.022 \times 10^{23} \text{ mol}^{-1}$), resulting in J/mol. According to Einstein's photoelectric equation, the minimum energy needed to remove one mole of electrons is the total photon energy minus the kinetic energy ($E_{photon} - KE$), yielding J/mol. Finally, dividing this by Avogadro's number gives the minimum energy for a single electron. This minimum energy corresponds to a maximum (threshold) wavelength $\lambda_0 = hc/E_{min}$ of nm.