Question 24: Dual Nature of Matter and Radiation

Question

Ultraviolet light of wavelength 99 mm falls on a metal plate of work function 1.0 eV. If the mass of the electron is 9.1 $$	imes$$ 10$$^{-31}$$ kg, the wavelength of the fastest photoelectron emitted is

Accepted Answer

Given
$$\begin{aligned}
& K_{\max }=h v-W_0 \
& =\frac{\left(6.6 	imes 10^{-34}ight) 	imes\left(3 	imes 10^8ight)}{99 	imes 10^{-9}}-1.0 	imes 1.6 	imes 10^{-19} \
& =2 	imes 10^{-18}-1.6 	imes 10^{-19} \
& =1.84 	imes 10^{-18} \mathrm{~J}
\end{aligned}$$
Now,
$$\begin{aligned}
\lambda & =\frac{h}{\sqrt{2 m K_{\max }}} \
& =\frac{6.6 	imes 10^{-34}}{\sqrt{2 	imes\left(9.1 	imes 10^{-31}ight) 	imes 1.84 	imes 10^{-18}}} \
& =0.36 	imes 10^{-9} \mathrm{~m}=0.36 \mathrm{~nm}
\end{aligned}$$

Answer

0.63 nm

Answer

0.66 nm

Answer

0.33 nm

Answer

0.36 nm

Dual Nature of Matter and Radiation

Ultraviolet light of wavelength 99 mm falls on a metal plate of work function 1.0 eV. If the mass of the electron is 9.1 $\times 10^{-31}$ kg, the wavelength of the fastest photoelectron emitted is

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