Question 369: Dual Nature of Matter and Radiation

Question

If the maximum kinetic energy of emitted electrons in photoelectric effect is $3.2 	imes 10^{-19} \mathrm{~J}$ and the work-function for metal is $6.63 	imes 10^{-19} \mathrm{~J}$, then stopping potential and threshold wavelength respectively are
[Planck's constant, $h=6.63 	imes 10^{34} \mathrm{~J}$-s]
[Velocity of light, $c=3 	imes 10^8 \frac{\mathrm{~m}}{\mathrm{~s}}$ ]
[Charge on electron $=1.6 	imes 10^{-19} \mathrm{C}$ ]

Accepted Answer

The maximum kinetic energy of emitted photoelectron is
$$K_{	ext {max }}=e V_s$$
where, $V_s=$ stopping potential.
$$\Rightarrow \quad V_s=\frac{K_{\max }}{	heta}=\frac{3.2 	imes 10^{-19}}{1.6 	imes 10^{-19}}=2 \mathrm{~V}$$
Also, the work-function of a metal is
$$\begin{aligned}
\phi & =\frac{1242}{\lambda_0(\mathrm{~nm})} \mathrm{eV} \
\lambda_0 & =\frac{1242 	imes 1.6 	imes 10^{-19}}{\phi} \mathrm{~nm}\
\begin{aligned}
\end{aligned}
\end{aligned}$$
$$\begin{aligned}
\Rightarrow \quad & =\frac{1242 	imes 1.6 	imes 10^{-19}}{6.63 	imes 10^{-19}} \mathrm{~nm} \
& \approx 3000\mathop A\limits^o
\end{aligned}$$

Answer

4V, 6000$\mathop A\limits^o$

Answer

3V, 4000$\mathop A\limits^o$

Answer

2V, 3000$\mathop A\limits^o$

Answer

1V, 1000$\mathop A\limits^o$

Dual Nature of Matter and Radiation

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