Question

Using Einstein’s photoelectric equation, the graph between the kinetic energy \( E \) of photoelectrons emitted and the frequency \( \nu \) of incident radiation is shown correctly in figure

• A. Graph (C)
• B. Graph (A)
• C. Graph (D)
• D. Graph (B)

Hint:

In photoelectric effect graphs, kinetic energy never starts from the origin; it starts from the threshold frequency.

Answer 1

The Correct Option is B

Step 1: Write Einstein’s photoelectric equation.
\[ E_{\text{max}} = h\nu - \phi \] where \( h \) is Planck’s constant and \( \phi \) is the work function.
Step 2: Identify nature of the graph.
The equation is linear in \( \nu \), so the graph of kinetic energy versus frequency is a straight line.
Step 3: Note important features of the graph.
- The slope of the graph is \( h \)
- The graph cuts the frequency axis at threshold frequency \( \nu_0 = \dfrac{\phi}{h} \)
- For \( \nu<\nu_0 \), no photoelectrons are emitted
Step 4: Analyze given options.
Only graph (A) shows a straight line with positive slope that intercepts the frequency axis at a non-zero value.
Step 5: Conclusion.
Graph (A) correctly represents Einstein’s photoelectric equation.