Light of wavelength _ ph falls on a cathode plate inside a vacuum… - Vidyadip

MCQ

Light of wavelength $\lambda_{\text {ph }}$ falls on a cathode plate inside a vacuum tc:be as shown in the figure. The work function of the cathode surface is $\phi$ and the anode is a wire mesh of conducting material kept at a distance $d$ from the cathode. A potential difference $V$ is maintained between the electrodes. If the minimum de Broglie wavelength of th: electrons passing through the anode is $\lambda_c$, which of the following statement($s$) is(are) true?

A
$\lambda_e$ decreases with increase in $\phi$ and $\lambda_{\text {ph }}$
B
$\lambda_c$ is approximately halved, if $d$ is doubled
✓
For large potential difference $(V \gg \phi / e), \lambda_e$ is approximately halved if $V$ is made four times
D
$\lambda_e$ increases at the same rate as $\lambda_{\text {ph }}$ for $\lambda_{\text {ph }} < h c / \phi$

✓

Answer

Correct option: C.

For large potential difference $(V \gg \phi / e), \lambda_e$ is approximately halved if $V$ is made four times

c
The correct option is A For large potential difference $\left(V \gg \frac{\phi}{e}\right), \lambda_e$ is approximately halved if V is made four times According to the conservation of energy principle,

$\frac{h c}{\lambda_{P h}}-\phi+e V=\frac{p_{\max }^2}{2 m}$

Now, the de-Broglie wavelength is given by,

$\lambda_e=\frac{h}{p_{\max }} \Rightarrow p_{\max }^2=\frac{h^2}{\lambda_e^2}$

$\therefore \frac{h c}{\lambda_{ Ph }}-\phi+e V=\frac{h^2}{2 m \lambda_e^2}$

When $V >> \frac{\phi}{e}$

$\Rightarrow \phi \ll e V \text { and } \frac{h c}{\lambda_{p h}}+e V=\frac{h^2}{2 m \lambda_e^2}$

$\Rightarrow \lambda_e \propto \frac{1}{\sqrt{V}}$

So, when $V$ is made four times, $\lambda_e$ is halved.

Hence, $(A)$ is the correct answer.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

At any instant, the velocity and acceleration of a particle moving along a straight line are $v$ and $a$. The speed of the particle is increasing if

Which of the following statement is true

$A$ ray of light is incident normally on the first refracting face of the prism of refracting angle $A$.The ray oflight comes out at grazing emergence.If one half of the prism (shaded position) is knocked off,the same ray will

Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6 \times 10^{-27}\,kg$ and radius of nucleus is $1.5 \times 10^{-15} A ^{1 / 3}\,m$. The approximate ratio of the nuclear density and water density is $n \times 10^{13}$. The value of $n$ is $.................$

If $250 \,J$ of work is done in sliding a $5 \,kg$ block up an inclined plane of height $4 \,m$. value of Work done against friction is ............. $J$ $\left(g=10 \,ms ^{-2}\right)$

The cause of the potential barrier in a $p-n$ junction diode is

A thin flexible wire of length $L$ is connected to two adjacent fixed points carries a current $I$ in the clockwise direction, as shown in the figure. When system is put in a uniform magnetic field of strength $B$ going into the plane of paper, the wire takes the shape of a circle. The tension in the wire is

The intensity distribution of $X-$ rays from two coolidge tubes operated on different voltages $V_1$ and $V_2$ and using different target materials of atomic numbers $Z_1$ and $Z_2$ is shown in the figure. Which one of the following inequalities is true?

For one complete cycle of a thermodynamic process on a gas as shown in the $P-V$ diagram, Which of following is correct

If the length of the simple pendulum is increased by $44\%$, then what is the change in time period of pendulum ..... $\%$