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Dual Nature of Radiation and Matter: questions with answers

Class 12 Physics, Chapter 11 (NCERT). 15 questions by concept, 1 with pictures. Open “Show answer” for the answer and why.

How to teach this chapter · Common misconceptions & worked visual for this chapter

Photocurrent, collection and intensity

Question 1

A photocell at saturation gives current I. The light frequency stays above the threshold frequency and the efficiency stays the same. Only the beam intensity is halved. Which claim is correct?

  1. (a)Current becomes 2I because electrons move faster
  2. (b)Current stays I because maximum electron energy stays the same
  3. (c)Current becomes I/2 because the electron emission rate halves
  4. (d)Current falls to zero because any dim beam is below threshold
Show answer

(c) Current becomes I/2 because the electron emission rate halves

Current measures charge per second, so half the photon arrival rate gives half the collected current.

Question 2

A photocell already collects every electron emitted by a fixed light beam. What happens when its positive collector voltage is increased further?

  1. (a)The photocurrent continues increasing in direct proportion to voltage
  2. (b)The work function becomes zero
  3. (c)Photoelectron emission frequency doubles
  4. (d)The steady photocurrent remains at its saturation value
Show answer

(d) The steady photocurrent remains at its saturation value

Once collection is complete, the fixed number emitted per second limits current.

Einstein energy balance and stopping potential

Question 3

The graph shows photocurrent for two light beams on the same emitter. What is the ratio of the maximum initial kinetic energies of photoelectrons, KA:KB?

-1.5-1.0-0.50+0.5+1.0ABIV(V)
  1. (a)3:1
  2. (b)√3:1
  3. (c)1:3
  4. (d)1:1
Show answer

(a) 3:1

Stopping magnitudes are 1.5 V and 0.5 V. Since Kmax=eV0, the maximum kinetic-energy ratio is 1.5:0.5=3:1.

Question 4

A metal has threshold wavelength 400 nm. Separate beams of wavelength 300 nm and 500 nm strike it in the single-photon regime. Which beams can eject electrons?

  1. (a)Both beams
  2. (b)Only the 500 nm beam
  3. (c)Neither beam
  4. (d)Only the 300 nm beam
Show answer

(d) Only the 300 nm beam

Emission needs hc/λ above φ=hc/400 nm. Only the shorter 300 nm wavelength supplies sufficient energy.

Question 5

A metal has work function 4.2 eV. Light of wavelength 330 nm is incident. Use hc=1240 eV nm. Which conclusion is correct?

  1. (a)Emission: wavelength exceeds the threshold wavelength
  2. (b)No emission: photon energy is about 3.76 eV, below the work function
  3. (c)No emission: photons have zero momentum
  4. (d)Emission: every photon supplies 8.0 eV
Show answer

(b) No emission: photon energy is about 3.76 eV, below the work function

Threshold wavelength is about 295 nm; 330 nm is longer and its photon energy is insufficient.

Photoelectric graph slopes and material thresholds

Question 6

The stopping magnitude V0 is plotted vertically against incident frequency ν horizontally. Which is the slope of the straight line above threshold?

  1. (a)h/e
  2. (b)hc
  3. (c)e/h
  4. (d)h
Show answer

(a) h/e

Divide eV0=hν−φ by e. The slope in voltage per frequency is h/e.

Question 7

An experiment gives stopping-voltage versus frequency slope s=4.12×10⁻¹⁵ V s. Which operation recovers Planck’s constant from this slope?

  1. (a)Multiply s by the elementary charge e
  2. (b)Use s itself as h
  3. (c)Divide s by e
  4. (d)Multiply s by the speed of light c
Show answer

(a) Multiply s by the elementary charge e

The slope equals h/e, so h=es≈6.59×10⁻³⁴ J s. Voltage-energy conversion needs the electron charge.

Surface escape, threshold and prompt photoemission

Question 8

A monochromatic beam with frequency above the threshold value is made much dimmer, without changing its frequency. Which statement describes the very first photoemission events?

  1. (a)The metal work function rises when the beam gets dimmer
  2. (b)Each photon loses frequency
  3. (c)They still start immediately, only fewer happen each second
  4. (d)Each electron must accumulate wave energy for a much longer time
Show answer

(c) They still start immediately, only fewer happen each second

Absorption of one sufficient-energy photon is prompt. Intensity changes the event rate.

Question 9

A classical model predicts an hours-long wait for an electron to collect energy from very dim above-threshold light. Which observation most directly contradicts that prediction?

  1. (a)Photoemission waits until continuous accumulation supplies the work function
  2. (b)Photoemission starts without an appreciable delay
  3. (c)Metals conduct electric current
  4. (d)Visible light can interfere
Show answer

(b) Photoemission starts without an appreciable delay

Prompt emission at low intensity contradicts the slow continuous-absorption picture.

Photon energy, momentum and photon flux

Question 10

At fixed total optical power, a laser wavelength is halved. Which happens to the number of photons emitted per second?

  1. (a)It stays constant
  2. (b)It becomes zero
  3. (c)It doubles
  4. (d)It halves
Show answer

(d) It halves

Halving wavelength doubles photon energy; the same energy per second then contains half as many photons.

Question 11

A photon in vacuum has nonzero energy E and zero rest mass. What is the magnitude of its momentum?

  1. (a)E/c²
  2. (b)Zero
  3. (c)E/c
  4. (d)Ec
Show answer

(c) E/c

For a photon E=pc. Zero rest mass does not imply zero momentum.

de Broglie wavelength and mechanical state

Question 12

A nonrelativistic particle's de Broglie wavelength is halved. By what factor must its kinetic energy increase?

  1. (a)4
  2. (b)2
  3. (c)8
  4. (d)1
Show answer

(a) 4

Since K=h²/(2mλ²), halving wavelength requires four times the kinetic energy.

Question 13

A proton and an alpha particle have the same nonrelativistic kinetic energy. Take mα=4mp. What is λα:λp?

  1. (a)2:1
  2. (b)1:1
  3. (c)1:2
  4. (d)1:4
Show answer

(c) 1:2

At equal K, wavelength varies as 1/√m. The four-times heavier alpha particle has half the wavelength.

Matter-wave evidence and macroscopic limits

Question 14

A neutron and an electron have equal nonzero momentum magnitudes. Which de Broglie wavelength comparison is correct?

  1. (a)Only the electron has a wavelength because the neutron is neutral
  2. (b)They have equal wavelengths
  3. (c)The neutron wavelength is necessarily longer because it is neutral
  4. (d)The neutron wavelength is 1836 times the electron wavelength
Show answer

(b) They have equal wavelengths

λ=h/p depends on momentum. Electric charge is not required.

Question 15

A beam of neutral atoms produces diffraction through suitable slits. Is this compatible with de Broglie’s relation?

  1. (a)No; neutral atoms must have zero momentum
  2. (b)Yes; diffraction first gives the atoms electric charge
  3. (c)No; only electrically charged beams can have matter waves
  4. (d)Yes; neutral atoms have momentum and therefore matter wavelength
Show answer

(d) Yes; neutral atoms have momentum and therefore matter wavelength

Matter-wave behaviour is not restricted to electrically charged particles.

Common misconception in Dual Nature of Radiation and Matter

Open full misconception guide →

Can brighter light always release photoelectrons?

Wrong

Light below the threshold frequency ejects electrons if it is bright enough.

Why it feels right. More light delivers more total energy.

Right

In the usual single-photon model, each photon needs energy at least equal to the metal's work function.

Worked example

Bright red
Many photons→Each below threshold→No photoelectrons
Dim blue
Fewer photons→Each above threshold→Photoelectrons possible
Brightness changes the number of photons. Each photon must still meet the energy threshold to eject an electron in this model.
  1. Take a metal for which red photons have energy below the work function and blue photons have energy above it.
  2. Brighter red light brings more photons, each still below threshold.
  3. Even dim blue light can release electrons.