A copper ball of radius 1 cm and work function 4.47 eV is irradiated with ultraviolet radiation of wavelength 2500 $$\text{Å}$$. The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is :

$$E = \frac{hc}{\lambda} = \frac{12420\text{ eV}\cdot\text{\AA}}{2500\text{ \AA}} \approx 4.97\text{ eV}$$

$$K_{max} = E - \phi = 4.97\text{ eV} - 4.47\text{ eV} = 0.50\text{ eV}$$

Since $$K_{max} = e V_0$$, the maximum positive potential the ball can reach before emission stops is $$V_0 = 0.50\text{ V}$$

The potential of a isolated conducting sphere of radius $$r$$ is given by:

$$V_0 = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r}$$

$$0.50 = \frac{9 \times 10^9 \times Q}{0.01}$$

$$0.50 = 9 \times 10^{11} \times Q$$

$$Q = \frac{0.50}{9 \times 10^{11}} \approx 0.0555 \times 10^{-11}\text{ C} = 5.55 \times 10^{-13}\text{ C}$$