Question

For two different photosensitive materials having work function and 2 respectively, are illuminated with light of sufficient energy to emit electrons. If the graph of stopping potential versus frequency is drawn, for these two different photosensitive materials the ratio of slope of graph for these two materials is

• A. 1:1
• B. 1:2
• C. 1:4
• D. 4:1

Answer 1

The Correct Option is A

The question involves the concept of photoelectric effect and the graphical relationship between stopping potential and frequency for two different photosensitive materials. To solve this problem, we need to understand the photoelectric equation and its representation on a graph.

According to the photoelectric effect, the energy of incident photons \(E = h\nu\), where \(h\) is Planck's constant and \(\nu\) is the frequency of the light. The kinetic energy of the emitted electron is given by:

\(E_k = h\nu - \phi\)

Where \(\phi\) is the work function of the material. The stopping potential \(V_0\) is related to the kinetic energy by:

\(eV_0 = h\nu - \phi\)

Rearranging gives us:

\(V_0 = \frac{h}{e}\nu - \frac{\phi}{e}\)

From the equation above, we can see that the graph of stopping potential \(V_0\) versus frequency \(\nu\) will be a straight line where:

• The slope is \(\frac{h}{e}\).
• The intercept is \(-\frac{\phi}{e}\).

Since the slope of the \(V_0\) vs. \(\nu\) graph is determined solely by \(\frac{h}{e}\) and not by the work function \(\phi\), the slope is the same for both materials, regardless of their work functions. Therefore, the ratio of the slopes for these two materials is:

Answer: \(1:1\)

This means the slope is the same for both, confirming that the correct answer is indeed 1:1.