Question

For photoelectric emission from certain metal, the cut-off frequency is $\nu .$ If radiation of frequency $2\nu$ impinges on the metal plate, the maximum possible velocity of the emitted electron will be-
[$m-$ is electron mass]

• A. $2\sqrt{\frac{h\nu }{m}}$
• B. $\sqrt{\frac{h\nu }{2m}}$
• C. $\sqrt{\frac{h\nu }{m}}$
• D. $\sqrt{\frac{2h\nu }{m}}$

Answer 1

The correct option is D $\sqrt{\frac{2h\nu }{m}}$

From Einstein's photoelectric equation,

$\frac{1}{2}m{v}_{max}^2=h\nu -\varphi$

$\frac{1}{2}m{v}_{\text{max}}^2=h\left(2\nu \right)-h\nu$

$\frac{1}{2}m{v}_{\text{max}}^2=h\nu$

$v_{\text{max}}=\sqrt{\frac{2h\nu }{m}}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.