Question 312: Dual Nature of Matter and Radiation

Question

A photosensitive metallic surface has work function $\phi$. If photon of energy $3 \phi$ falls on the surface, the electron comes out with a maximum velocity of $6 	imes 10^6 \mathrm{~m} / \mathrm{s}$. When the photon energy is increased to $9 \phi$, then maximum velocity of photoelectrons will be

Accepted Answer

For photoelectric effect,
$$\mathrm{K} . \mathrm{E}_{\max }=\mathrm{E}-\phi_0\quad	ext{.... (i)}$$
Given: $E_1=3 \phi_0$ and $E_2=9 \phi_0$
From (i),
$$\begin{aligned}
& \mathrm{K} . \mathrm{E}_1=3 \phi_0-\phi_0=2 \phi_0 \
& \mathrm{~K} \cdot \mathrm{E}_2=9 \phi_0-\phi_0=8 \phi_0
\end{aligned}$$
But, $K \cdot E_1=\frac{1}{2} m v_1^2$ and $K \cdot E_2=\frac{1}{2} m v_2^2$
$$\begin{aligned}
	herefore\quad& \frac{\mathrm{K} \cdot \mathrm{E}_1}{\mathrm{~K} \cdot \mathrm{E}_2}=\frac{\mathrm{v}_1^2}{\mathrm{v}_2^2}=\frac{1}{4} \
	herefore\quad& \mathrm{v}_2=2 \mathrm{v}_1 \
& \mathrm{v}_2=2 	imes 6 	imes 10^6=12 	imes 10^6 \mathrm{~m} / \mathrm{s}
\end{aligned}
$$

Answer

$12 	imes 10^6 \mathrm{~m} / \mathrm{s}$

Answer

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

Answer

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

Answer

$24 	imes 10^6 \mathrm{~m} / \mathrm{s}$

Dual Nature of Matter and Radiation

A photosensitive metallic surface has work function \phi. If photon of energy 3 \phi falls on the surface, the electron comes out with a maximum velocity of 6 \times 10^6 \mathrm{~m} / \mathrm{s}. When the photon energy is increased to 9 \phi, then maximum velocity of photoelectrons will be

Choose the correct answer: