Question

According to Einstein's interpretation of the photoelectric effect, the maximum K.E. of photoelectrons depends on ( h -W) where is the frequency of incident radiation and W is the work function. For three different metals graph plotted between maximum K/E. and the frequency of incident radiations. The three graphs obtained:

• A. have different slopes but constant intercept on y axis
• B. are all parallel to y axis but at different heights
• C. same slope but different intercept on y axis
• D. none of these

Answer 1

The correct option is C same slope but different intercept on y axis

According to Einstein's equation,

$h\nu =W+{K.E}_{max}$

$K.E{.}_{max}=h\nu -W$

Comparing it with equation of straight line with slope $m$ and intercept $c$,

$y=mx+c$

We see that on taking $K.E_{max}$ on $y-axis$ and frequency of incident radiation on $x-axis$ , we get a straight line with intercept $W=workfunction$ and slope $h=\text{Planck's constant}$

We see that while plotting the graph of $K.E.$ vs $\nu$ for 3 different metals , slope will be same as $h$ is same for all 3 metals. But $W$ is different for different metals . So intercept will be different for different metals.