According to Einstein's photoelectric equation, the plot of the Kinetic Energy of the emitted photoelectrons from a metal versus the frequency of the incident radiation gives a straight line whose slope:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → is the same for all metals and independent of the intensity of the radiation
Einstein's photoelectric equation gives the maximum kinetic energy of the photoelectrons:
\( \displaystyle K_{\mathrm{max}} = h\nu - \phi_0 \)
Plotted against \( \nu \), this is a straight line of slope \( h \) (Planck's constant) and intercept \( -\phi_0 \) on the energy axis. Planck's constant is a universal constant, so the slope is the same for every metal and does not depend on the intensity. Only the work function \( \phi_0 \) (and so the threshold frequency, where the line meets the frequency axis) changes from metal to metal.
Option (1) depends on the nature of the metal used — Incorrect. The metal changes only the intercept \( \phi_0 \), not the slope.
Option (2) depends on the intensity of the radiation — Incorrect. Intensity changes only the number of photoelectrons.
Option (3) depends both on the intensity of the radiation and the metal used — Incorrect. Neither the metal nor the intensity changes the slope.
NCERT (2026-27):
Einstein’s Photoelectric Equation: Energy Quantum of Radiation – “… Using Eq. (11.1), the photoelectric equation, Eq. (11.2), can be written as
\( \displaystyle e V_0 = h\nu - \phi_0 ; \quad \text{for } \nu \ge \nu_0 \)
This is an important result. It predicts that the V0 versus ν curve is a straight line with slope = (h/e), independent of the nature of the material.”