A polished copper sphere of radius 5.0 cm hangs on an insulating thread in a large vacuum chamber…

Step 1. Photon energy (a). $E = \dfrac{hc}{\lambda} = \dfrac{6.63 \times 10^{-34}\ \text{J s} \times 3.0 \times 10^{8}\ \text{m/s}}{200 \times 10^{-9}\ \text{m}} = 9.945 \times 10^{-19}\ \text{J} = 6.22\ \text{eV}$.

Step 2. Fastest electron (b). $K_{\max} = 6.22\ \text{eV} - 4.65\ \text{eV} = 1.57\ \text{eV}$. (The light is well above copper's threshold, $\lambda_0 = hc/\phi = 267\ \text{nm}$.)

Step 3. Final potential (c). An electron leaving the surface with $K_{\max}$ just fails to escape when $eV = K_{\max}$. So $V = 1.57\ \text{V}$.

Step 4. Charge (d, e). $Q = \dfrac{RV}{k} = \dfrac{0.05\ \text{m} \times 1.566\ \text{V}}{9.0 \times 10^{9}\ \text{N m}^2\text{/C}^2} = 8.70\ \text{pC}$. That is $Q/e = 5.44 \times 10^{7}$ electrons.

Step 5. Least time (f). The lamp delivers $\dfrac{2.0 \times 10^{-6}\ \text{W}}{9.945 \times 10^{-19}\ \text{J}} = 2.01 \times 10^{12}$ photons per second, so $2.01 \times 10^{8}$ electrons leave per second at first (a current of $32.2\ \text{pA}$). Later, slow electrons are pulled back, so the real time is longer. The least time is $\dfrac{5.44 \times 10^{7}}{2.01 \times 10^{8}\ \text{s}^{-1}} = 0.27\ \text{s}$.

Step 6. The larger sphere (g). It reaches the same potential, $1.57\ \text{V}$, but its capacitance is twice as large, so $Q = 17.4\ \text{pC}$.