In the experimental study of photoelectric effect, a graph of stopping potential versus frequency of incident radiation for two metals A and B is plotted and identical slopes for both are obtained with different cut off frequencies \( (\nu_{0B} \gt \nu_{0A}) \). So
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Slope for all metals is same = \( h/e \). Here work function of B > work function of A
Einstein's photoelectric equation links the stopping potential \( V_0 \) to the frequency \( \nu \) of the incident light.
\( \displaystyle eV_0 = h\nu - \phi_0 \;\Rightarrow\; V_0 = \frac{h}{e}\,\nu - \frac{\phi_0}{e} \)
This is a straight line of \( V_0 \) against \( \nu \) with slope \( h/e \), which contains only universal constants, so it is the same for every metal.
At the cut-off frequency \( V_0 = 0 \), so the work function is \( \phi_0 = h\nu_0 \). A larger cut-off frequency means a larger work function.
\( \displaystyle \nu_{0B} \gt \nu_{0A} \;\Rightarrow\; \phi_{B} \gt \phi_{A} \)
Why the other options are incorrect
Option (1) Slope for all metals is same = \( h/e \). Here work function of A > work function of B — Incorrect. The slope is right, but the order of the work functions is reversed.
Option (3) Slope for all metals is same = \( h \). Here work function of A > work function of B — Incorrect. The slope of the \( V_0 \)-\( \nu \) graph is \( h/e \), not \( h \); \( h \) would be the slope of an energy (\( eV_0 \)) against frequency graph. The work-function order is also reversed.
Option (4) Slope for all metals is same = \( h \). Here work function of B > work function of A — Incorrect. The work-function order is right, but the slope of a stopping-potential graph is \( h/e \), not \( h \).
NCERT (2026-27):
Einstein’s Photoelectric Equation: Energy Quantum of Radiation – “… Equation (11.3) shows that the greater the work function φ0, the higher the minimum or threshold frequency ν0 needed to emit photoelectrons.”
Einstein’s Photoelectric Equation: Energy Quantum of Radiation – “… 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.”