A faint ultraviolet lamp gives an intensity of 2.0 × 10⁻³ W/m² on a metal plate with a work…

Step 1. The power. $P = IA = 2.0 \times 10^{-3}\ \text{W/m}^2 \times 2.5 \times 10^{-19}\ \text{m}^2 = 5.0 \times 10^{-22}\ \text{W}$.

Step 2. The energy. $2.0\ \text{eV} = 2.0 \times 1.6 \times 10^{-19}\ \text{J} = 3.2 \times 10^{-19}\ \text{J}$.

Step 3. The time. $t = \dfrac{3.2 \times 10^{-19}\ \text{J}}{5.0 \times 10^{-22}\ \text{W}} = 640\ \text{s}$. That is about eleven minutes.

Step 4. The factor. $\dfrac{640\ \text{s}}{10^{-9}\ \text{s}} = 6.4 \times 10^{11}$.