Question

A light of wavelength $\lambda$ falls on metal having work function $\frac{hc}{{\lambda }_o}$. The photoelectric effect will take place only if:

• A. $\lambda$ $\ge$ ${\lambda }_{\circ }$
• B. $\lambda$ $\le$ ${\lambda }_{\circ }$
• C. $\lambda$ $=$ $2{\lambda }_{\circ }$
• D. $\lambda =\frac{{\lambda }_o}{2}$

Answer 1

The correct option is B $\lambda$ $\le$ ${\lambda }_{\circ }$

The formula of photoelectric effect is given by:
h$\nu$ = $w$ + KE.
where, $w$ = work function
$w$ = h${\nu }_o$
Therefore, ${\lambda }_o$, is the wavelength corresponding to ${\nu }_o$. Similarly, $\lambda$ is the wavelength corresponding to $\nu$.
We know that kinetic energy in the photoelectric equation varies from 0 to any positive number.
Hence, h$\nu \ge w$
And so is,$\frac{hc}{\lambda }\ge \frac{hc}{{\lambda }_{\circ }}$
And ultimately, $\lambda \le {\lambda }_{\circ }$

Therefore, correct option is (b)