Question 341: Dual Nature of Matter and Radiation

Question

When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are $$\mathrm{v}_1$$ and $$\mathrm{v}_2$$ respectively. The ratio $$\mathrm{v}_1: \mathrm{v}_2$$ is

Accepted Answer

$$\begin{array}{ll} 
& K . E_{\max }=h v-\phi_0 \
& 	ext { Given, } \
& E_1=2 \phi_0 	ext { and } E_2=3 \phi_0 \
\Rightarrow & K \cdot E_1=2 \phi_0-\phi_0=\phi_0 \
\Rightarrow & K \cdot E_2=3 \phi_0-\phi_0=2 \phi_0 \
& 	ext { but, } K \cdot E_1=\frac{1}{2} m v_1^2 	ext { and } K \cdot E_2=\frac{1}{2} m_2^2 \
	herefore \quad & \frac{K \cdot E_1}{K \cdot E_2}=\frac{v_1^2}{v_2^2}=\frac{1}{2} \
	herefore \quad & \frac{v_1}{v_2}=\frac{1}{\sqrt{2}}
\end{array}$$

Answer

$$\sqrt{2}: 1$$

Answer

$$\sqrt{3}: 1$$

Answer

$$\sqrt{3}: \sqrt{2}$$

Answer

$$1: \sqrt{2}$$

Dual Nature of Matter and Radiation

When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are $\mathrm{v}_1 and \mathrm{v}_2 respectively. The ratio \mathrm{v}_1: \mathrm{v}_2$ is

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