In photoelectric effect, the stopping potential ( $\mathrm{V}_{0}$ ) v/s frequency (v) curve is plotted. ( h is the Planck's constant and $\phi_{0}$ is work function of metal) (A) $\mathrm{V}_{0} \mathrm{v} / \mathrm{s} v$ is linear (B) The slope of $\mathrm{V}_{0} \mathrm{v} / \mathrm{s} v$ curve $=\frac{\phi_{0}}{\mathrm{~h}}$ (C) h constant is related to the slope of $\mathrm{V}_{0} \mathrm{v} / \mathrm{s} v$ line (D) The value of electric charge of electron is not required to determine h using the $\mathrm{V}_{0} \mathrm{v} / \mathrm{s} v$ curve. (E) The work function can be estimated without knowing the value of $h$. Choose the correct answer from the options given below :

JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Modern Physics

In photoelectric effect, the stopping potential (

V_{0}

) v/s frequency (v) curve is plotted.
( h is the Planck's constant and

ϕ_{0}

is work function of metal)
(A)

V_{0} v / s v

is linear
(B) The slope of

V_{0} v / s v

curve

= \frac{ϕ _{0}}{h}

V_{0} v / s v

line
(D) The value of electric charge of electron is not required to determine h using the

V_{0} v / s v

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

h

.

Choose the correct answer from the options given below :

Answer: (C)

The photoelectric equation is

h ν = ϕ_{0} + e V_{0}

, which rearranges to

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

This has the form

y = m x + c

, so a plot of

V_{0}

against

ν

is a straight line — statement (A) is correct.

The slope of this line is

\frac{h}{e}

, not

\frac{ϕ _{0}}{h}

— so statement (B) is wrong.

Since slope

= \frac{h}{e}

, measuring the slope and knowing the electronic charge

e

gives

h

; so

h

is indeed obtainable from the slope of this line — statement (C) is correct.

Because the slope equals

h / e

, extracting

h

from the slope requires knowing

e

— so statement (D), which claims

e

is not needed, is wrong.

The y-intercept of the line is

- ϕ_{0} / e

; knowing

e

, the work function

ϕ_{0}

can be read off directly from this intercept without ever needing the value of

h

— statement (E) is correct.

So the correct statements are (A), (C) and (E) only.

JEE Main · 2025 · 24 Jan 2025 · Shift 2 · Single correct option