Concepts Of Physics MCQ Edition [Volume 2]PhysicsPhotoelectric Effect and Wave–Particle Duality
A silver ball of radius 4.8 cm is suspended by a thread within a vacuum chamber. Ultraviolet light having a wavelength of 200 nm strikes the ball for a duration such that a total light energy of 1.0 10⁻⁷ J is received on the surface. If, on average, one photon out of every ten thousand successfully ejects a photoelectron, determine the electric potential at the surface of the ball (taking the potential at infinity as
Options
- A0.3 V at the surface, 0.3 V at the centre
- B3.0 V at the surface, 3.0 V at the centre
- C3.0 V at the surface, 0 V at the centre
- D0.3 V at the surface, 0 V at the centre
Correct answer
A. 0.3 V at the surface, 0.3 V at the centre
Step-by-step solution
The energy of a single incident photon is given by: E = hc = 6.63 10⁻³⁴ 3 10^8 200 10⁻⁹ = 9.945 10⁻¹⁹ J The total number of photons striking the surface is: n = E_ total E = 1.0 10⁻⁷ 9.945 10⁻¹⁹ 1.005 10¹¹ Given that one out of every 10^4 photons ejects a photoelectron, the total number of ejected electrons is: n_e = n 10⁻⁴ = 1.005 10¹¹ 10⁻⁴ = 1.005 10^7 The total positive charge developed on the silver ball due to the emission of electrons is: q = n_e e = 1.005 10^7 1.6 10⁻¹⁹ 1.608 10⁻¹² C The electric potential a