JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Modern Physics

light of wavelength

λ_{ph}

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 statement(s) is(are) true?

(A) $λ_{e}$ decreases with increase in $ϕ$ and $λ_{ph}$
(B) $λ_{e}$ is approximately halved, if $d$ is doubled
(C)For large potential difference $(V ≫ ϕ / e), λ_{e}$ is approximately halved if $V$ is made four times✓ Correct
(D) $λ_{e}$ increases at the same rate as $λ_{ph}$ for $λ_{ph} < h c / ϕ$

Answer: (C)

Solution

Energy equation:

\frac{h c}{λ _{p h}} + e V - ϕ = \frac{p _{ma x}^{2}}{2 m} = \frac{h ^{2}}{2 m λ _{e}^{2}}

For

V ≫ ϕ / e

, the work function and photon energy terms become negligible:

e V \approx \frac{h ^{2}}{2 m λ _{e}^{2}}

This gives

λ_{e} \propto \frac{1}{V}

When V is made 4 times,

λ_{e}

becomes

\frac{1}{2}

(halved).

Option (C) is correct. The distance

d

does not appear in the energy equation, so (B) is incorrect.

JEE Advanced · 2016 · 22 May 2016 · Paper 2 · One or more correct options