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Dual Nature of Radiation question

2024 · 30 Jan · Shift 2 · Q71

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Dual Nature of Radiation
2024 · 30 Jan · Shift 2 · Q71

Dual Nature of Radiation question

2024 · 30 Jan · Shift 2 · Q71

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1

For the photoelectric effect, the maximum kinetic energy

\left(E_k\right)

of the photoelectrons is plotted against the frequency

(v)

of the incident photons as shown in figure. The slope of the graph gives JEE Main 2024 (Online) 30th January Evening Shift Physics - Dual Nature of Radiation Question 36 English

JEE Main 2024 (Online) 30th January Evening Shift Physics - Dual Nature of Radiation Question 36 English

A
Planck's constant
B
Work function of the metal
C
Charge of electron
D
Ratio of Planck's constant to electric charge

View written solutionFree

Correct answer: A

For photoelectric effect, Einstein’s photoelectric equation is $E_k^{\max}=h\nu-\phi$ where:

$E_k^{\max}$ = maximum kinetic energy of emitted photoelectrons
$h$ = Planck’s constant
$\nu$ = frequency of incident radiation
$\phi$ = work function of the metal

Compare this with the equation of a straight line: $y=mx+c$ Here,

$y \equiv E_k^{\max}$
$x \equiv \nu$
slope $m = h$
intercept $c = -\phi$

Therefore, when maximum kinetic energy is plotted against frequency, the slope of the graph is $h$ which is Planck’s constant.
Check options:

A: Planck's constant ✅ Correct
B: Work function of the metal ❌ This is related to the intercept, not slope
C: Charge of electron ❌ Not the slope here
D: Ratio of Planck's constant to electric charge ❌ This would appear if stopping potential were plotted against frequency

Hence, the correct answer is A.

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