Dual Nature of Radiation and Matter: Class 12 Important Questions with Answers

Practice set: test yourself

Try every question before looking at the answers below. 64 or more out of 80 means you are ready for the board.

C. Very short answer (1 mark each)

1. Define threshold frequency.
2. Define stopping potential.
3. Which metal has the lowest work function?
4. Name the scientist who verified Einstein's equation.
5. Write the energy of a photon of wavelength λ.
6. What does the saturation current depend on?
7. Give one failure of the wave theory.
8. Two particles have the same p. Compare λ.
9. Why is the photon number not conserved?
10. Express 1 eV in joules.

D. Short answer I (2 marks each)

1. Draw I–V graphs for two intensities at the same frequency.
2. Write Einstein's photoelectric equation and explain each term.
3. φ₀ = 2.0 eV, λ = 300 nm: find K_max and V₀.
4. Find the photons per second from a 5 mW laser of 600 nm.
5. An electron and a proton have the same KE. Which has the larger λ? Why?
6. Explain why the photoelectric effect supports the photon model.
7. Draw V₀–ν for two metals; mark ν₀ and φ₀/e.
8. Find λ of an electron moving at 10⁶ m/s.

Rough work

E. Short answer II (3 marks each)

1. State the laws of photoelectric emission and explain them using Einstein's equation.
2. Show how h and φ₀ are found from the V₀–ν graph.
3. A proton and an α-particle are accelerated through the same V. Ratio of their λ, momenta and KE?
4. Light of 5 × 10¹⁴ Hz and 8 × 10¹⁴ Hz falls on a metal with ν₀ = 4 × 10¹⁴ Hz. Ratio of maximum speeds?
5. Why does the wave theory fail to explain the photoelectric effect? Give three reasons.
6. Derive λ = h/√(2mqV) for a charged particle accelerated from rest.

F. Long answer (5 marks each)

1. Describe an experiment to study the photoelectric effect. Draw and explain the effect of (a) intensity and (b) frequency on the photocurrent. Find V₀ for 250 nm light on a metal of φ₀ = 3.0 eV.
2. Explain de Broglie's hypothesis. Derive λ for an electron accelerated through V. Compare λ of an electron and a proton of the same KE of 100 eV.

G. HOTS (higher-order thinking)

1. Can a metal show the photoelectric effect with infrared light? Why or why not?
2. Why is the stopping potential independent of the intensity?
3. If the frequency is doubled, does K_max double? Explain.
4. Why don't we see the wave nature of a moving car?

20 MCQs

1. Photon energy of 620 nm light
   (a) 1 eV (b) 3 eV (c) 2 eV (d) 4 eV
2. K_max depends on
   (a) frequency and φ₀ (b) intensity (c) time (d) area
3. Slope of V₀–ν graph
   (a) h (b) e/h (c) φ₀ (d) h/e
4. Photocurrent depends on
   (a) frequency only (b) intensity (c) work function only (d) nothing
5. φ₀ = 2 eV: threshold wavelength
   (a) 310 nm (b) 620 nm (c) 1240 nm (d) 200 nm
6. de Broglie λ
   (a) hp (b) h/m (c) p/h (d) h/p
7. Electron λ after 400 V
   (a) 0.06 nm (b) 0.123 nm (c) 1.2 nm (d) 0.6 nm
8. Same KE: λ largest for
   (a) α (b) proton (c) electron (d) neutron
9. Photon momentum
   (a) hλ (b) λ/h (c) hc/λ (d) h/λ
10. Equal intensity: more photons per second in
    (a) blue (b) red (c) violet (d) UV
11. Stopping potential depends on
    (a) intensity (b) area (c) ν (d) distance
12. Emission below ν₀
    (a) none (b) slow (c) fast (d) depends on intensity
13. Same momentum: λ_p : λ_α
    (a) 2 : 1 (b) 1 : 1 (c) 1 : 2 (d) 4 : 1
14. Photon energy 4 eV, φ₀ = 2.5 eV: V₀
    (a) 6.5 V (b) 4 V (c) 1.5 V (d) 2.5 V
15. Field emission uses
    (a) heat (b) sound (c) light (d) strong electric field
16. Who explained the photoelectric effect
    (a) Einstein (b) Millikan (c) Hertz (d) de Broglie
17. If KE is made 9 times, λ becomes
    (a) λ/3 (b) 9λ (c) 3λ (d) λ/9
18. Photoelectrons have speeds
    (a) all equal (b) c (c) zero (d) from 0 to v_max
19. Rest mass of a photon
    (a) h/c (b) zero (c) m_e (d) hν/c²
20. Lowest work function
    (a) Pt (b) Cu (c) Cs (d) Fe

1 (c) · 2 (a) · 3 (d) · 4 (b) · 5 (b) · 6 (d) · 7 (a) · 8 (c) · 9 (d) · 10 (b) · 11 (c) · 12 (a) · 13 (b) · 14 (c) · 15 (d) · 16 (a) · 17 (a) · 18 (d) · 19 (b) · 20 (c)

Assertion–Reason (6)

(a) Both true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.

1. A: The stopping potential does not change with intensity. R: K_max depends only on ν for a given metal.
2. A: Photoelectric emission is instantaneous. R: One photon gives all its energy to one electron.
3. A: A cricket ball shows wave nature. R: Every moving body has a de Broglie wavelength.
4. A: K_max of photoelectrons increases with intensity. R: More photons fall per second.
5. A: An electron and a photon of the same λ have the same momentum. R: p = h/λ for both.
6. A: Red light can't eject electrons from zinc. R: Red photons have less energy than zinc's work function.

Key: 1 (a) · 2 (a) · 3 (d) · 4 (d) · 5 (a) · 6 (a)

Answers to the practice set