Question

A plot of kinetic energy of emitted photoelectrons from a metal versus the frequency of incident radiation gives a straight line, the intercept of which:

• A. Depends on the nature of the metal used
• B. Depends on the intensity of radiation
• C. Depends both on the intensity and the nature of metal used
• D. Is a constant and is same for all metals which is independent of the intensity of incident radiation

Hint:

In photoelectric effect, slope of \(K_{\max}\) vs \(\nu\) graph gives Planck’s constant, while intercept gives work function (metal dependent).

Answer 1

The Correct Option is A

Step 1: Write Einstein’s photoelectric equation.
\[ K_{\max} = h\nu - \phi \]
where \(\phi\) is the work function of the metal.

Step 2: Compare with straight line equation.
\[ K_{\max} = h\nu - \phi \]
This is of the form \(y = mx + c\), where:
- Slope = \(h\)
- Intercept on energy axis = \(-\phi\)

Step 3: Interpret intercept.
The intercept depends on \(\phi\), which is the work function of the metal.

Step 4: Nature of work function.
Work function is a property of the material (metal), hence it depends on the nature of the metal used.

Step 5: Effect of intensity.
Intensity affects number of electrons emitted, not their maximum kinetic energy. Hence intercept does not depend on intensity.

Step 6: Conclusion.
Intercept depends only on the nature of the metal used.

Step 7: Final answer.
\[ \boxed{\text{Depends on the nature of the metal used}} \]