Question 331: Dual Nature of Matter and Radiation

Question

When wavelength of incident radiation on the metal surface is reduced from '$\lambda_1$' to '$\lambda_2$', the kinetic energy of emitted photoelectrons is tripled. The work function of metal [$\mathrm{h}=$ Plank's constant, $\mathrm{c}=$ velocity of light]

Accepted Answer

Let $\mathrm{K}$ represent kinetic energy
$\begin{aligned}
	herefore \quad \mathrm{K}_1 & =\frac{\mathrm{hc}}{\lambda_1}-\mathrm{W}_0 \
	ext { and } & \mathrm{K}_2=\frac{\mathrm{hc}}{\lambda_2}-\mathrm{W}_0 \
\mathrm{~K}_2 & =3 \mathrm{~K}_1
\end{aligned}$
$\begin{aligned}
& 	herefore \quad \frac{h c}{\lambda_2}-W_0=3 \frac{h c}{\lambda_1}-3 W_0 \
& 	herefore \quad 2 W_0=\frac{3 h c}{\lambda_1}-\frac{h c}{\lambda_2} \
& 	herefore \quad W_0=\frac{h c}{2}\left(\frac{3 \lambda_2-\lambda_1}{\lambda_1 \lambda_2}ight)
\end{aligned}$

Answer

$\frac{\mathrm{hc}}{2}\left[\frac{3 \lambda_1-\lambda_2}{\lambda_1 \lambda_2}\right]$

Answer

$\frac{\mathrm{hc}}{2}\left[\frac{3 \lambda_2-\lambda_1}{\lambda_1 \lambda_2}\right]$

Answer

hc $\left[\frac{3 \lambda_1-\lambda_2}{\lambda_1 \lambda_2}\right]$

Answer

hc $\left[\frac{3 \lambda_2-\lambda_1}{\lambda_1 \lambda_2}\right]$

Dual Nature of Matter and Radiation

When wavelength of incident radiation on the metal surface is reduced from '\lambda_1' to '\lambda_2', the kinetic energy of emitted photoelectrons is tripled. The work function of metal [\mathrm{h}= Plank's constant, \mathrm{c}= velocity of light]

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