According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal Vs the frequency, of the incident radiation gives as straight the whose slope

is the same for the all metals and independent of the intensity of the radiation

depends both on the intensity of the radiation and the metal used

depends on the intensity of the radiation

depends on the nature of the metal used

Dual Nature of Radiation PYQ — JEE Main 2004 · Shift 0 · Q122 with Solution

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Correct answer: D

Write Einstein’s photoelectric equation

The maximum kinetic energy of emitted photoelectrons is $K_{\max} = h\nu - \phi$ where:
- $h$ = Planck’s constant
- $\nu$ = frequency of incident radiation
- $\phi$ = work function of the metal
Compare with equation of a straight line

A straight line is written as $y = mx + c$

Here, if we plot kinetic energy $K_{\max}$ on the $y$ -axis versus frequency $\nu$ on the $x$ -axis, then $K_{\max} = h\nu - \phi$

So,
- slope $m = h$
- intercept $c = -\phi$
Interpret the slope

Since the slope is $h$ , and Planck’s constant is universal, the slope:
- does not depend on the metal
- does not depend on the intensity of radiation
Check the options
- A: depends both on intensity and metal used — Incorrect
- B: depends on intensity — Incorrect
- C: depends on nature of metal used — Incorrect
- D: is the same for all metals and independent of intensity — Correct
Final answer

The slope of the graph is $h$ which is the same for all metals and independent of intensity of incident radiation.