Question

In photoelectric effect the graph of stopping potential ($V_0$) versus frequency ($\nu$) is a straight line. The slope of this graph is ______.

• A. $h$
• B. $\frac{e}{h}$
• C. $\frac{V_0}{e}$
• D. $\frac{h}{e}$

Hint:

The slope of this graph is a \textbf{Universal Constant}. It does not matter what metal you use for the cathode; the slope ($h/e$) will always be the same.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Einstein's photoelectric equation relates the maximum kinetic energy of electrons to the incident photon energy and the work function ($\phi_0$).
Step 2: Formula Application:
$K_{max} = h\nu - \phi_0$ Since $K_{max} = eV_0$, we can write: $eV_0 = h\nu - \phi_0 \implies V_0 = \left(\frac{h}{e}\right)\nu - \frac{\phi_0}{e}$
Step 3: Explanation:
Comparing this with the straight-line equation $y = mx + c$, the variable on the y-axis is $V_0$ and on the x-axis is $\nu$. The slope $m$ is therefore $h/e$.
Step 4: Final Answer:
The slope of the graph is $h/e$.