A monochromatic light of wavelength λ is incident on a metallic plate of work function φ. An electron is emitted normally from point A with maximum kinetic energy and enters a uniform magnetic field B perpendicular to its initial velocity. It follows a circular path and hits the plate again at B. The distance AB is:
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Question

A monochromatic light of wavelength λ is incident on a metallic plate of work function φ. An electron is emitted normally from point A with maximum kinetic energy and enters a uniform magnetic field B perpendicular to its initial velocity. It follows a circular path and hits the plate again at B. The distance AB is:

Options

G1 Physics · Accepted Answer

Maximum photoelectron kinetic energy is K(max) = hc/λ - φ. Thus (1/2)mv² = hc/λ - φ ⇒ mv = √[2m(hc/λ - φ)]. In magnetic field B perpendicular to velocity, the electron moves in a circle of radius r = mv/(eB) = √[2m(hc/λ - φ)]/(eB). The electron starts from the plate and returns to it after a semicircular path, so the separation AB is the diameter: AB = 2r = √[8m(hc/λ - φ)]/(eB). Correct option: C.