JEE Main 2025 Jan 24 Shift 2, Physics Q12: Introduction and Photoelectric Effect

JEE Main2025Jan 24, Shift 2Physics

In photoelectric effect, the stopping potential $(V_{0})$ v/s frequency $(ν)$ curve is plotted.

( $h$ is the Planck's constant and $ϕ_{0}$ is work function of metal)

(A) $V_{0}$ v/s $ν$ is linear

(B) The slope of $V_{0}$ v/s $ν$ curve $= \frac{ϕ _{0}}{h}$

(D) The value of electric charge of electron is not required to determine $h$ using the $V_{0}$ v/s $ν$ curve.

(E) The work function can be estimated without knowing the value of $h$ .

Choose the correct answer from the options given below :

Solution

Using Einstein's photoelectric equation,

$e V_{0} = h ν - ϕ_{0}$

or,

$V_{0} = \frac{h}{e} ν - \frac{ϕ _{0}}{e}$

Comparing with the equation of a straight line, $y=mx+c$:

Slope $=\dfrac{h}{e}$ and y-intercept $=-\dfrac{\phi_0}{e}$.

(A) $V_0$ v/s $\nu$ is linear. Correct.

(B) Slope is $\dfrac{\phi_0}{h}$. Actually, slope $=\dfrac{h}{e}$. Incorrect.

(C) Since slope $=\dfrac{h}{e}$, $h$ is related to the slope. Correct.

(D) To determine $h$, $h=e\times$(slope). Hence the value of $e$ is required. Incorrect.

(E) Since y-intercept $=-\dfrac{\phi_0}{e}$, the work function is given by

$ϕ_{0} = - e \times (y-intercept) .$

Thus, the value of $h$ is not required (only the value of $e$ is needed). Hence, (E) is correct.

Note: The y-intercept is obtained by extrapolating the straight line, since photoelectric emission occurs only for $\nu \ge \nu_0$.

Correct options: $\boxed{\text{(A), (C) and (E)}}$

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