Question 272: Dual Nature of Matter and Radiation

Question

For two different photosensitive materials having work function $\phi$ and $2 \phi$ 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

Accepted Answer

Step 1: Recall the photoelectric equation
EinsteinÃ¢ÂÂs photoelectric equation is:
$ K_{\max} = h f - \phi $
Stopping potential $V_0$ is:
$ e V_0 = K_{\max} = h f - \phi $
So:
$ V_0 = \frac{h}{e} f - \frac{\phi}{e} $
This shows $V_0$ versus $f$ is a
straight line
of the form:
$ V_0 = \left(\frac{h}{e}ight) f - \frac{\phi}{e}. $
Step 2: Slope of the line
The slope is:
$ 	ext{slope} = \frac{h}{e} $
which is
independent
of the materialÃ¢ÂÂs work function $\phi$.
Step 3: Compare the two materials
Material 1 has work function $\phi$.
Material 2 has work function $2\phi$.
Their lines will have different intercepts (threshold frequency shifts), but the
slopes are the same
.
Hence, the ratio of slopes:
$ 1 : 1. $
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Correct Answer: Option A Ã¢ÂÂ $1 : 1$

Answer

$1: 1$

Answer

$1: 2$

Answer

$1: 4$

Answer

$4: 1$

Dual Nature of Matter and Radiation

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