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Dual Nature of Radiation and Matter – Class 12 Physics notes, important questions and MCQs

NCERT Class 12 Physics, chapter 11. Notes, key terms, important questions with answers and MCQs.

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Chapter overview

Light behaves as particles (photons) in the photoelectric effect, and matter shows wave nature (de Broglie waves).

Photoelectric effect

Einstein's equation: hν = φ₀ + K_max, K_max = eV₀ (stopping potential).
Threshold frequency ν₀ = φ₀/h; no emission below it, however intense the light.
Photocurrent ∝ intensity; K_max depends on frequency, not intensity.

Matter waves

de Broglie wavelength λ = h/p = h/(mv).
For an electron accelerated through V volts: λ = 1.227/√V nm.
Davisson–Germer experiment confirmed electron diffraction.

Key terms

Work function: minimum energy needed to remove an electron from a metal surface
Stopping potential: negative potential that just stops the fastest photoelectrons
Threshold frequency: minimum frequency of light that can eject electrons from a given metal

Formulas

hν = φ₀ + ½mv²_max
λ = h/p
E = hν, h = 6.63 × 10⁻³⁴ J s

Important questions with answers

Why can't the wave theory of light explain the photoelectric effect?2 marks

Wave theory predicts that intensity, not frequency, decides electron energy and that there would be a time delay at low intensity, and no threshold frequency. Experiments show a threshold frequency, energy depending on frequency only, and instant emission.

Write Einstein's photoelectric equation and explain each term.3 marks

hν = φ₀ + Kmax. hν is the energy of one photon; φ₀ = hν₀ is the work function, the minimum energy needed to free an electron; Kmax = ½mv²max is the maximum kinetic energy of emitted electrons. Below ν₀ no emission occurs.

Describe the Davisson–Germer experiment and what it proved. Find the de Broglie wavelength of a 1 kg ball moving at 10 m/s and explain why we do not see its wave nature.5 marks

Electrons accelerated through 54 V were scattered from a nickel crystal; a strong scattered beam at 50° matched diffraction from crystal planes with λ ≈ 0.165 nm, close to the de Broglie value 0.167 nm. It confirmed that electrons (matter) have wave nature. For the ball, λ = h/mv = 6.63 × 10⁻³⁴/(1 × 10) = 6.63 × 10⁻³⁵ m, far smaller than any object or slit, so its wave effects cannot be observed.

Quick revision

Below threshold frequency, no photoemission.
λ = h/mv.
Davisson–Germer showed matter waves.

Exam tips

Increasing intensity increases the number of photoelectrons, not their maximum energy.
Kmax = hν − φ₀ = eV₀; plot of V₀ versus ν is a straight line with slope h/e.

Practice MCQs

Energy of a photon is
1. h/ν
2. hλ
3. hν
4. ν/h
Show answer
Answer: (c) hν. E = hν.
de Broglie wavelength is
1. p/h
2. hp
3. h/p
4. h × m
Show answer
Answer: (c) h/p. λ = h/p.
Increasing light intensity (frequency fixed above threshold) increases
1. K_max
2. photocurrent
3. work function
4. threshold frequency
Show answer
Answer: (b) photocurrent. More photons.
Davisson–Germer experiment demonstrated
1. photoelectric effect
2. nuclear fission
3. wave nature of electrons
4. X-ray production
Show answer
Answer: (c) wave nature of electrons. Electron diffraction.
de Broglie wavelength of an electron accelerated through 100 V is about
1. 1.23 nm
2. 12.3 nm
3. 0.123 nm
4. 0.0123 nm
Show answer
Answer: (c) 0.123 nm. 1.227/√V nm.
Work function 2 eV, photon energy 5 eV. Stopping potential is
1. 2 V
2. 3 V
3. 5 V
4. 7 V
Show answer
Answer: (b) 3 V. K_max = 3 eV.
An electron accelerated through 100 V has λ about
1. 1.227 nm
2. 0.1227 nm
3. 12.27 nm
4. 0.01227 nm
Show answer
Answer: (b) 0.1227 nm. 1.227/√100.
Light of energy 5 eV falls on a metal of work function 2 eV. Stopping potential is
1. 2 V
2. 3 V
3. 5 V
4. 7 V
Show answer
Answer: (b) 3 V. 5 − 2 = 3 eV.

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Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.