PhysicsCBSE Class 12 · Board exam 2023, set 55/1/1 · 3 marks · Short answer

CBSE Class 12 Physics 2023: question 29

Set in the CBSE Class 12 board exam of 2023, paper 55/1/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerDual Nature of Radiation and Matter

How does Einstein's photoelectric equation explain the emission of electrons from a metal surface ? Explain briefly.
Plot the variation of photocurrent with :
(a) collector plate potential for different intensity of incident radiation, and
(b) intensity of incident radiation.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/1/1.

Hints

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

Hint 1

One photon gives all its energy to one electron — what must that energy exceed?

Hint 2

Does intensity change the stopping potential or only the number of electrons?

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.

Einstein's equation: $K_{ma x} = h ν - ϕ_{0}$ . Light consists of photons of energy $h ν$ ; an electron absorbs one whole photon. If $h ν$ exceeds the work function $ϕ_{0}$ (minimum energy to escape), the electron is emitted and the excess energy appears as its maximum kinetic energy. If $h ν < ϕ_{0}$ (i.e. $ν < ν_{0}$ ), no emission occurs however intense the light; emission is instantaneous.
1 mark
(a) Graph (described): photocurrent (y-axis) vs collector plate potential (x-axis) for intensities $I_{3} > I_{2} > I_{1}$ at fixed frequency. Each curve rises with positive potential and becomes flat at a saturation current; higher intensity gives higher saturation current. On the negative side all curves fall to zero at the same stopping potential $- V_{0}$ .
1 mark
(b) Graph (described): photocurrent vs intensity of incident radiation (frequency fixed above threshold) is a straight line through the origin — photocurrent is directly proportional to intensity.
1 mark

Answer: $K_{ma x} = h ν - ϕ_{0}$ ; (a) saturation current rises with intensity, same stopping potential; (b) straight line through origin.

Where the marks are

Explanation via photon absorption and $K_{ma x} = h ν - ϕ_{0}$ (1 mark)
Graph of photocurrent vs collector potential for different intensities with common stopping potential (1 mark)
Linear graph of photocurrent vs intensity (1 mark)

Revise the chapter

Chapter: Dual Nature of Radiation and Matter (notes, formulas, where marks are lost and every past question)
Topic: Einstein's Photoelectric Equation

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 paper2023 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2023: question 29

Hints

Step-by-step solution

Revise the chapter

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