Skip to content
Question of 83

Q.[Case study] In an experiment with two different photosensitive metals, the plot of photo-current (II) versus collector plate potential (VV) was obtained as shown in the figure below. The frequency and intensity of incident light was constant.

(a) What conclusion can be drawn about the work functions of metals A and B from the graph? Explain.
Meghalaya MboseMBOSE Meghalaya Intermediate Board 2026Subjective· 2mImportance★★★★★
0% · 0/83 Questions
🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Applying Einstein's photoelectric equation at the stopping potential for each metal, and using the fact that both are illuminated by light of the same frequency, shows that the metal requiring the larger-magnitude stopping potential has the smaller work function — so here, Metal B (needing −V2-V_2) has the smaller work function and Metal A (needing only −V1-V_1) has the larger one.

Einstein's photoelectric equation at the stopping potential

For light of frequency ν\nu incident on a metal of work function ϕ\phi, the maximum kinetic energy of the emitted photoelectrons is:

KEmax⁡=hν−ϕKE_{\max}=h\nu-\phi

At the stopping potential VsV_s, exactly enough retarding potential energy is applied to stop even the most energetic photoelectrons: eVs=KEmax⁡eV_s=KE_{\max}, so:

eVs=hν−ϕ  ⟹  Vs=hνe−ϕeeV_s = h\nu-\phi \quad\implies\quad V_s=\frac{h\nu}{e}-\frac{\phi}{e}

Applying this to metals A and B

Both metals are illuminated by light of the same frequency ν\nu (stated in the problem), so the term hν/eh\nu/e is identical for both:

Vs(A)=hνe−ϕAe=V1V_s(A)=\frac{h\nu}{e}-\frac{\phi_A}{e}=V_1

Vs(B)=hνe−ϕBe=V2V_s(B)=\frac{h\nu}{e}-\frac{\phi_B}{e}=V_2

From the graph, Metal B's photocurrent falls to zero only at the more negative potential −V2-V_2, i.e. V2>V1V_2>V_1 — B needs a bigger stopping potential than A.

What this says about the work functions

Subtracting the two equations:

V2−V1=ϕA−ϕBeV_2-V_1=\frac{\phi_A-\phi_B}{e}

Since V2>V1V_2>V_1 (left side positive), we need ϕA−ϕB>0\phi_A-\phi_B>0, i.e.

ϕA>ϕB\phi_A>\phi_B

…

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests

Full access for 14 days. No credit card required.