Question

From the figure describing photoelectric effect, we may infer correctly that

• A. Na and Al both have the same threshold frequency
• B. Maximum kinetic energy for both the metals depends linearly on the frequency
• C. The stopping potential are different for Na and Al for the same change in frequency
• D. Al is better photosensitive material than Na

Hint:

In photoelectric effect, the slope of the stopping potential vs frequency graph is the same for all materials as it is equal to Planck’s constant \( h/e \). The difference in intercepts indicates different work functions.

Answer 1

The Correct Option is B

From Einstein’s photoelectric equation: \[ K_{\text{max}} = h\nu - \phi \] where \( K_{\text{max}} \) is the maximum kinetic energy, \( h \) is Planck's constant, \( \nu \) is the frequency of incident light, and \( \phi \) is the work function. The stopping potential \( V \) is directly proportional to \( K_{\text{max}} \), so the equation becomes: \[ eV = h\nu - \phi \] This implies a linear relationship between the stopping potential \( V \) and the frequency \( \nu \). In the given graph, both Na and Al exhibit straight lines, confirming that \( V \) (and hence \( K_{\text{max}} \)) varies linearly with frequency for both metals.