SATHEE: Modern Physics 4 Question 9

Modern Physics 4 Question 9

9. Light of wavelength $λ_{p h}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $φ$ 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 the electrons passing through the anode is $λ_{e}$ , which of the following statements(s) is (are) true?

(2016 Adv.)

(a) $λ_{e}$ increases at the same rate as $λ_{p h}$ for $λ_{p h} < h c / φ$

(b) $λ_{e}$ is approximately halved, if $d$ is doubled

(d) For large potential difference $(V ≫ φ / e), λ_{e}$ is approximately halved if $V$ is made four times.

Show Answer

Solution:

$K_{max} = \frac{h c}{λ_{p h}} - φ$

Kinetic energy of electron reaching the anode will be

$K = \frac{h c}{λ_{p h}} - φ + e V$

Now, $λ_{e} = \frac{h}{\sqrt{2 m K}} = \frac{h}{\sqrt{2 m \frac{h c}{λ_{p h}} - φ + e V}}$

$\begin{aligned} If e V ≫ φ then, λ_{e} = \frac{h}{\sqrt{2 m \frac{h c}{λ_{p h}} + e V}} \\ If V_{f} = 4 V_{i} then, {(λ_{e})}_{f} ≃ \frac{{(λ_{e})}_{i}}{2} \end{aligned}$

Modern Physics 4 Question 9

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Modern Physics 4 Question 9

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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