Chapter Review

The work function ($W_0$) for the caesium atom is $1.9\text{ eV}$. Calculate: (a) the threshold wavelength $\lambda_0$ (b) the threshold frequency $\nu_0$

If irradiated with light of wavelength $\lambda = 500\text{ nm}$, calculate the kinetic energy ($KE$) and velocity ($v$) of the ejected photoelectron.

Constants: $1\text{ eV} = 1.602 \times 10^{-19}\text{ J}$, $h = 6.626 \times 10^{-34}\text{ J s}$, $c = 3.0 \times 10^8\text{ m/s}$, $m_e = 9.1 \times 10^{-31}\text{ kg}$.

Emission transitions in the Paschen series end at orbit $n = 3$ and start from orbit $n$. The transition frequency is given by the formula: $\nu = 3.29 \times 10^{15} \left( \frac{1}{3^2} - \frac{1}{n^2} \right)\text{ Hz}$

Calculate the value of $n$ if the transition is observed at a wavelength of $1285\text{ nm}$.