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For photoelectric emission from certain metal the cut-off frequency is ν. If radiation of frequency 2ν impinges on the metal plate, the maximum possible velocity of the emitted electron will be (m is the electron mass)

1. √hν/m
2. 2√hν/m
3. 2√hν/(2m)
4. √hν/(2m)

Correct answer: √hν/m

Solution

The maximum kinetic energy of the emitted electron is given by Einstein's photoelectric equation: K.E. = h(f - f₀), where f is the incident frequency and f₀ is the cut-off frequency. Substituting f = 2ν and f₀ = ν, we get K.E. = hν. The maximum velocity is then v = √(2K.E./m) = √(2hν/m).

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