During an experiment on the photoelectric effect, light of wavelength 400 nm illuminates a cesium plate at a rate of 5.0 W . The potential of the collector plate is kept sufficiently positive relative to the emitter to ensure the current attains its saturation value. Given that, on average, one out of every 10^6 incident photons succeeds in ejecting a photoelectron, determine the photocurrent in the circuit.

Step-by-step solution

The energy of a single incident photon is given by: E = hc Substituting the given values: E = 6.63 10⁻³⁴ 3 10^8 400 10⁻⁹ 4.97 10⁻¹⁹ J The number of photons incident on the plate per second is: N = P E = 5.0 4.97 10⁻¹⁹ 1.0 10¹⁹ s ⁻¹ Since one out of every 10^6 photons ejects a photoelectron, the number of photoelectrons emitted per second is: n = N 10⁻⁶ = 1.0 10¹⁹ 10⁻⁶ = 1.0 10¹³ s ⁻¹ The saturation photocurrent is the total charge of these electrons per unit time: I = ne = 1.0 10¹³ 1.6 10⁻¹⁹ = 1.6 10⁻⁶ A = 1.6 A