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

$square root of fraction numerator hv over denominator left parenthesis 2 straight m right parenthesis end fraction end root$
$square root of hv over straight m end root$
$square root of fraction numerator 2 hv over denominator straight m end fraction end root$
$2 square root of hv over straight m end root$

Solution

square root of fraction numerator 2 hv over denominator straight m end fraction end root

As space 1 half mv subscript max superscript 2 space equals space hv rightwards double arrow space straight v subscript max superscript 2 space equals space fraction numerator 2 hv over denominator straight m end fraction space therefore comma straight v subscript max space equals space square root of fraction numerator 2 hv over denominator straight m end fraction end root

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