The figure shows a graph between stopping potential and frequency of incident radiation for some metal surface. Study the graph and answer the following questions. a. What are the values of threshold frequency and threshold wavelength? [use c = 3 x10⁸m/s] b. Obtain the value of Planck's constant from the graph. c. The metal surface is illuminated by the radiation of frequency 10¹⁵ Hz. What would be the maximum kinetic energy of the emitted electrons?

The figure shows a graph between stopping potential and frequency of incident radiation for some metal surface. Study the graph and answer the following questions.

a. What are the values of threshold frequency and threshold wavelength? [use c = 3 x108 m/s]  

b. Obtain the value of Planck's constant from the graph. 

c. The metal surface is illuminated by the radiation of frequency 10¹⁵ Hz. What would be the maximum kinetic energy of the emitted electrons? 

Solution:

(a) From the graph, Threshold Frequency (f₀)=0.50 x 10¹⁵Hz

Threshold wavelength =\[\lambda  = \frac{c}{{{f_0}}} = \frac{{3 \times {{10}^8}}}{{0.50{\rm{ }} \times {\rm{ }}{{10}^{15}}}} = 6 \times {10^{ - 7}}\]

And slope = tanθ = $\frac{{Perp.}}{{Base}}$

$= \frac{3}{{(1.25 - 0.50) \times {{10}^{15}}}}$=4 x 10^-15

(b) We know, Plank’s Constant (h) = e x Slope of the graph = (1.6 x 10^-19)

=1.6 x 10 ^-19 x 4 x 10^-15

=6.4 x 10^-34Js

(c) Einstein's equation for photoelectric effect is given by,

 E_k​(max)=hf−hf₀  = 6.4 x 10^-34 x 1.25 x 10¹⁵ - 6.4 x 10^-34  x 0.50 x 10¹⁵

= 4.8 x 10^-19Joule

In an experiment on photoelectric effect, maximum K.E. (E_k) and frequency (f) is found to be straight line as shown in the figure. Compare the value of threshold frequency and Plank’s Constant.