Logo
Jeeify
MCQEasyJEE 2023Einstein's Equation

JEE Physics 2023 Question with Solution

The work functions of Aluminium and Gold are 4.1 eV4.1 \, \text{eV} and 5.1 eV5.1 \, \text{eV} respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is

  • A

    11

  • B

    22

  • C

    1.241.24

  • D

    1.51.5

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: The work functions are 4.1 eV4.1 \, \text{eV} for Aluminium and 5.1 eV5.1 \, \text{eV} for Gold.

Find: The ratio of the slopes of the stopping potential versus frequency plots for Gold and Aluminium.

Using Einstein's photoelectric equation,

K.Emax=eVs=hf−ϕ0K.E_{\text{max}} = eV_s = hf - \phi_0

so,

Vs=hef−ϕ0e.V_s = \frac{h}{e}f - \frac{\phi_0}{e}.

Comparing this with the straight-line form,

Vs=mf+c,V_s = mf + c,

the slope is

m=he.m = \frac{h}{e}.

Therefore, the slope is the same for all metals and is independent of the work function ϕ0\phi_0. Hence,

mGoldmAluminium=1.\frac{m_{\text{Gold}}}{m_{\text{Aluminium}}} = 1.

Therefore, the correct ratio is 11, which corresponds to option A.

Common mistakes

  • Using the work function values to compare slopes is incorrect because ϕ0\phi_0 affects the intercept, not the slope. Use the coefficient of ff in the equation Vs=hef−ϕ0eV_s = \frac{h}{e}f - \frac{\phi_0}{e}.

  • Confusing the stopping potential versus frequency graph with a kinetic energy versus frequency graph can lead to wrong interpretation. First write the linear equation explicitly and then identify slope and intercept separately.

Practice more Einstein's Equation questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trialMore on Einstein's Equation

Related questions