Question 259: Dual Nature of Matter and Radiation

Question

A photosensitive surface has work function $\phi$. If photon of energy $3 \phi$ falls on this surface, the electron comes out with maximum velocity of $4 	imes 10^6 \mathrm{~m} / \mathrm{s}$ When photon energy is increased to $7 \phi$ then maximum velocity of photoelectron will be

Accepted Answer

For photoelectric effect,
$$ \mathrm{K} \cdot \mathrm{E}_{\max }=\mathrm{E}-\phi \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)$$
Given: $\mathrm{E}_1=3 \phi$ and $\mathrm{E}_2=7 \phi$
From (i),
$$ \begin{aligned} & K \cdot E_1=3 \phi-\phi=2 \phi \ & K \cdot E_2=7 \phi-\phi=6 \phi \ & B u t, K \cdot E_1=\frac{1}{2} m v_1^2 	ext { and } K \cdot E_2=\frac{1}{2} m v_2^2 \ 	herefore \quad & \frac{K \cdot E_1}{K \cdot E_2}=\frac{v_1^2}{v_2^2}=\frac{1}{3} \ 	herefore \quad & v_2=\sqrt{3} v_1 \ & v_2=4 \sqrt{3} 	imes 10^6 \mathrm{~m} / \mathrm{s} \end{aligned} $$

Answer

$4 \sqrt{3} 	imes 10^6 \mathrm{~m} / \mathrm{s}$

Answer

$2 \sqrt{3} 	imes 10^6 \mathrm{~m} / \mathrm{s}$

Answer

$4 \sqrt{3} 	imes 10^3 \mathrm{~m} / \mathrm{s}$

Answer

$2 \sqrt{3} 	imes 10^3 \mathrm{~m} / \mathrm{s}$

Dual Nature of Matter and Radiation

A photosensitive surface has work function \phi. If photon of energy 3 \phi falls on this surface, the electron comes out with maximum velocity of 4 \times 10^6 \mathrm{~m} / \mathrm{s} When photon energy is increased to 7 \phi then maximum velocity of photoelectron will be

Choose the correct answer: