JEE Physics 2025 Question with Solution

Given: The statements are about the graph of stopping potential $V_0$ versus frequency $\nu$ in the photoelectric effect.

Find: Which set of statements is correct.

Using Einstein's photoelectric equation,

$$eV_0 = h\nu - \phi_0$$

So,

$$V_0 = \frac{h}{e}\nu - \frac{\phi_0}{e}$$

This shows that $V_0$ varies linearly with $\nu$.

Therefore, statement (A) is true.

From the same equation, the slope of the $V_0$ versus $\nu$ graph is

$$\text{slope} = \frac{h}{e}$$

So statement (B) is false because the slope is not $\frac{\phi_0}{h}$.

Since the slope is $\frac{h}{e}$, Planck's constant $h$ is related to the slope. Therefore, statement (C) is true.

To determine $h$ from the slope, the value of electron charge $e$ is required because

$$h = e \times \text{slope}$$

Hence statement (D) is false.

The work function can be obtained from the intercept only when the required constants are known. Thus statement (E) is false.

So the correct statements are (A) and (C) only, but the provided options and the solution identify the intended correct option as C, corresponding to (A), (B) and (C) only. This reflects a discrepancy in the source explanation.

Therefore, the correct option according to the source is C.

Given: A graph of stopping potential $V_0$ against frequency $\nu$ is considered.

Find: Which listed statements match the graph relation.

The kinetic energy relation is

$$E_{\text{kin}} = h\nu - \phi_0$$

and stopping potential satisfies

$$E_{\text{kin}} = eV_0$$

Combining,

$$eV_0 = h\nu - \phi_0$$

Rearranging,

$$V_0 = \frac{h}{e}\nu - \frac{\phi_0}{e}$$

Now compare each statement:

1. (A) says $V_0$ versus $\nu$ is linear. This is true.
2. (B) says the slope is $\frac{\phi_0}{h}$. From the equation, the slope is $\frac{h}{e}$, so this is false.
3. (C) says $h$ is related to the slope. This is true.
4. (D) says electron charge is not required to determine $h$. Since slope $= \frac{h}{e}$, this is false.
5. (E) says work function can be estimated without knowing $h$. This is false in the stated context.

Hence the physically consistent set is (A) and (C) only, but that set is absent in the options. The solution and source answer both mark option C as correct, so the extracted answer is C with the source discrepancy noted.

Therefore, the correct option as per the solution's is C.