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Question

A small metal plate of work function ϕ is kept at a distance d from a singly ionised, fixed ion. A monochromatic light beam is incident on the metal plate and photo electrons are emitted.Find the maximum wavelength of the light beam so that some of the electrons may go around the ion along a circle.

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Solution

(12mv2)max=hcλϕ
for the electron to move around the ion(fixed)

12mv2=PE+K

=e24πε0d+e28πε0d

Thus

e28πε0d=hcλϕ

or e2=hc8πε0dλ8πε0ϕd

or λ=8πε0hcde2+8πε0ϕd=e28πε0d

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