A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials (V_s). The graph shows the variation of stopping potential (V_s) with the frequency of incident radiation () for metals A and B. Answer the following questions : (I) From the graph, the work functions of A and B are (h is Planck’s constant and e value of charge on an electron) (II) For radiation of frequency > _2 incident on the surfaces of A and B, the maximum kinetic energy of ejected electron is (III) If the intensity of the incident radiation for both metals A and B, is doubled keeping its frequency constant, then (IV) The threshold frequency for a metal surface is _0. If the radiation of frequency 3_0 illuminates the surface, the maximum kinetic energy (KE) of photoelectrons is E_1. If the frequency were increased to 6_0, the maximum KE of the photoelectrons becomes E_2. Then ((E_1)/(E_2) ) equals (IV) Let m be the slope of the graph line for metal B. If e is the value of electron charge, then Planck’s constant ‘h’ is given by

PhysicsCBSE Class 12 · Board exam 2026, set 55/1/1 · 4 marks · Case-based

CBSE Class 12 Physics 2026: question 30

Set in the CBSE Class 12 board exam of 2026, paper 55/1/1, section D, question 30, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 4 marks · Case-basedCompetency-basedDual Nature of Radiation and Matter

A researcher performs an experiment on photo-electric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the value of corrosponding stopping potentials ( $V_{s}$ ). The graph shows the variation of stopping potential ( $V_{s}$ ) with the frequency of incident radiation ( $ν$ ) for metals A and B.
Answer the following questions :

(I)
From the graph, the work functions of A and B are (h is Planck’s constant and e value of charge on an electron)
1. (A) $ν_{1}$ and $ν_{2}$
2. (B) $V_{1}$ and $V_{2}$
3. (C) $h ν_{1}$ and $h ν_{2}$
4. (D) $\frac{h ν _{1}}{e}$ and $\frac{h ν _{2}}{e}$
1 mark
(II)
For radiation of frequency $ν > ν_{2}$ incident on the surfaces of A and B, the maximum kinetic energy of ejected electron is
1. (A)greater for metal A because it has a smaller work function.
2. (B)greater for metal B because it has a larger work function.
3. (C)greater for metal B because it has higher threshold frequency.
4. (D)the same for both metal A and metal B because it is independent of work functions of metals.
1 mark
(III)
If the intensity of the incident radiation for both metals A and B, is doubled keeping its frequency constant, then
1. (A)the slope of the parallel lines will increase.
2. (B)the slope of the parallel lines will decrease.
3. (C)the threshold frequencies for both A and B will decrease.
4. (D)the slope of the parallel lines will not change but more electrons will be emitted per second.
1 mark
(IV)
The threshold frequency for a metal surface is $ν_{0}$ . If the radiation of frequency $3 ν_{0}$ illuminates the surface, the maximum kinetic energy (KE) of photoelectrons is $E_{1}$ . If the frequency were increased to $6 ν_{0}$ , the maximum KE of the photoelectrons becomes $E_{2}$ . Then $(\frac{E _{1}}{E _{2}})$ equals
1. (A)1/3
2. (B)1/2
3. (C)2/5
4. (D)3/4
1 mark
OR
(IV)
Let m be the slope of the graph line for metal B. If e is the value of electron charge, then Planck’s constant ‘h’ is given by
1. (A)me
2. (B) $\frac{1}{m e}$
3. (C) $\frac{m}{e}$
4. (D) $\frac{e}{m}$
1 mark

Figure in the paper: Graph of stopping potential $V_{s}$ (vertical axis) versus frequency $ν$ (horizontal axis) with two parallel straight lines A and B. Line A cuts the frequency axis at $ν_{1}$ and line B at a larger $ν_{2}$ ( $ν_{1} < ν_{2}$ ). Extended dashed portions meet the negative $V_{s}$ axis at $V_{1}$ (for A) and $V_{2}$ (for B), with $V_{2}$ more negative. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 55/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Write Einstein's equation in the form $e V_{s} = h ν - ϕ_{0}$ .

Hint 2

Compare it with $y = m x + c$ to read off the slope and intercepts.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(I) Threshold frequencies are $ν_{1}$ (A) and $ν_{2}$ (B), and $ϕ_{0} = h ν_{0}$ . The work functions are therefore $h ν_{1}$ and $h ν_{2}$ . Option (C).
1 mark
(II) $K_{ma x} = h ν - ϕ_{0}$ . Since $ϕ_{A} < ϕ_{B}$ , $K_{ma x}$ is greater for A. Option (A).
1 mark
(III) Intensity affects only the number of photons. The slope $h / e$ and the threshold frequencies stay the same, but more electrons are emitted per second. Option (D).
1 mark
(IV)(a) $E_{1} = h (3 ν_{0}) - h ν_{0} = 2 h ν_{0}$ and $E_{2} = 6 h ν_{0} - h ν_{0} = 5 h ν_{0}$ , so $\frac{E _{1}}{E _{2}} = \frac{2}{5}$ . Option (C).
(IV)(b) $V_{s} = \frac{h}{e} ν - \frac{ϕ _{0}}{e}$ , so the slope is $m = \frac{h}{e}$ and $h = m e$ . Option (A).
1 mark

Answer: (I) C; (II) A; (III) D; (IV) C [or alternative: A]

Where the marks are

(I) hν₁ and hν₂, C (1 mark)
(II) Greater for A, A (1 mark)
(III) Slope unchanged, more electrons emitted, D (1 mark)
(IV) 2/5, C; or alternative h = me, A (1 mark)

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Chapter: Dual Nature of Radiation and Matter (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Dual Nature of Radiation and Matter, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2026: question 30

Hints

Step-by-step solution

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