Question 303: Dual Nature of Matter and Radiation

Question

A photoelectric surface is illuminated successively by monochromatic light of wavelength ' $\lambda$ ' and $\left(\frac{\lambda}{2}\right)$. If the maximum kinetic energy of the emitted photoelectrons in the first case is one-fourth that in the second case, the work function of the surface of the material is ( $\mathrm{c}=$ speed of light, $\mathrm{h}=$ Planck's constant$)$

Accepted Answer

$$\begin{aligned}
& \mathrm{E}_1=\frac{\mathrm{hc}}{\lambda}-\phi \quad	ext{.... (i)}\
& \mathrm{E}_2=\frac{\mathrm{hc}}{\lambda / 2}-\phi=\frac{2 \mathrm{hc}}{\lambda}-\phi\quad	ext{.... (ii)}
\end{aligned}$$
Given, $\mathrm{E}_1=\frac{\mathrm{E}_2}{4}$
$$	herefore \quad 4 \mathrm{E}_1=\mathrm{E}_2\quad	ext{.... (iii)}$$
From (ii) and (iii),
$$\begin{aligned}
& 4 \mathrm{E}_1=\frac{2 \mathrm{hc}}{\lambda}-\phi \
& 4\left(\frac{\mathrm{hc}}{\lambda}-\phiight)=\frac{2 \mathrm{hc}}{\lambda}-\phi \quad	ext{.... [Substituting from (i)]}
\end{aligned}$$
$$\begin{array}{ll}
	herefore & \frac{4 h c}{\lambda}-4 \phi=\frac{2 h c}{\lambda}-\phi \
	herefore & 3 \phi=\frac{2 h c}{\lambda} \
	herefore & \phi=\frac{2 h c}{3 \lambda}
\end{array}$$

Answer

$\frac{2 \mathrm{hc}}{\lambda}$

Answer

$\frac{\mathrm{hc}}{\lambda}$

Answer

$\frac{2 h \mathrm{c}}{3 \lambda}$

Answer

$\frac{\mathrm{hc}}{3 \lambda}$

Dual Nature of Matter and Radiation

Choose the correct answer: