Case Study Questions for Class 12 Physics Chapter 11 Dual Nature of Radiation and Matter

Case Study Questions for Class 12 Physics Chapter 11 Dual Nature of Radiation and Matter

Case Study Question 1:

According to wave theory of light, the light of any frequency can emit electrons from metallic surface provided the intensity of light be sufficient to provide necessary energy for emission of electrons, but according to experimental observations, the light of frequency less than threshold frequency cannot emit electrons; whatever be the intensity of incident light. Einstein also proposed that electromagnetic radiation is quantized.

If photoelectrons are ejected from a surface when light of wavelength λ₁ = 550 nm is incident on it. The stopping potential for such electrons is V_s =0.19 . Suppose the radiation of wavelength λ₂ = 190 nm is incident on the surface.

(i) Photoelectric effect supports quantum nature of light because
(A) there is a minimum frequency of light below which no photoelectrons are emitted.
(B) the maximum K.E. of photoelectric depends only on the frequency of light and not on its intensity.
(C) even when the metal surface is faintly illuminated, the photo electrons leave the surface immediately.
(D) electric charge of the photoelectrons is quantized.
(a) A, B, C
(b) B, C
(c) C, D
(d) A, D, C

(ii) In photoelectric effect, electrons are ejected from metals, if the incident light has a certain minimum
(a) wavelength
(b) frequency
(c) amplitude
(d) angle of incidence

(iii) Calculate the stopping potential V_s2 of surface.
(a) 4.47
(b) 3.16
(c) 2.76
(d) 5.28

(iv) Calculate the work function of the surface.
(a) 3.75
(b) 2.07
(c) 4.20
(d) 3.60

(v) Calculate the threshold frequency for the surface.
(a) 500 x 10¹² Hz
(b) 480 x 10¹³ Hz
(c) 520 x 10¹¹ Hz
(d) 460 x 10¹³ Hz

Answers and Explanations:

(i) Correct Option: (a) A, B, C

Explanation: • A: Below a certain minimum frequency, no electrons are emitted, showing the quantized nature of light. • B: Maximum kinetic energy depends only on frequency, not intensity, which also supports photon theory. • C: Photoelectron emission is instantaneous, even at low intensity. • D is incorrect because quantization of electron charge is not related to quantum nature of light.

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(ii) Correct Option: (b) frequency

Explanation: Photoemission occurs only when the frequency of light exceeds the threshold frequency. Intensity, amplitude, or angle do not govern emission.

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(iii) Correct Option: (a) 4.47 V

Explanation: Using Einstein’s equation: eV_s2 = hc(1/λ₂ − 1/λ₁) + eV_s1. Substituting values for λ₁ = 550 nm, λ₂ = 190 nm, and V_s1 = 0.19 V gives V_s2 ≈ 4.47 V.

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(iv) Correct Option: (b) 2.07 eV

Explanation: Φ = (hc/λ₁) − eV_s1. Calculating with λ₁ = 550 nm and V_s1 = 0.19 V gives Φ ≈ 2.07 eV.

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(v) Correct Option: (a) 500 × 10¹² Hz

Explanation: f₀ = Φ / h. With Φ ≈ 2.07 eV, f₀ ≈ 5 × 10¹⁴ Hz = 500 × 10¹² Hz.

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Chapter Notes (Colourful Handwritten Notes)

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