A monochromatic light beam of wavelength 330 nm and intensity 6.0 W m ⁻² falls normally on a photoelectric surface of area 1 cm ^2 . If the quantum efficiency of the surface is 1 % (i.e., 1 % of the incident photons successfully eject an electron), the saturation photocurrent is (Take h = 6.6 10⁻³⁴ J s , c = 3 10^8 m s ⁻¹ , and e = 1.6 10⁻¹⁹ C )

Step-by-step solution

Energy of a single incident photon is: E = hc = 6.6 10⁻³⁴ 3 10^8 330 10⁻⁹ = 19.8 10⁻²⁶ 330 10⁻⁹ = 6 10⁻¹⁹ J Total power incident on the surface is: P = I A = 6.0 (1 10⁻⁴) = 6.0 10⁻⁴ W The number of photons incident per second n is: n = P E = 6.0 10⁻⁴ 6 10⁻¹⁹ = 10¹⁵ s ⁻¹ Since the quantum efficiency is 1 % , the number of electrons ejected per second n_e is: n_e = 1 100 n = 10¹³ s ⁻¹ The saturation photocurrent i is the total charge of these electrons: i = n_e e = 10¹³ 1.6 10⁻¹⁹ = 1.6 10⁻⁶ A i = 1.6 ; A . Answer: 1.