Case Study Questions for Class 12 Physics Chapter 11 Dual Nature of Radiation and Matter
Case Study Question 1:
Table of Contents
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 Vs =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 Vs2 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.
(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.
(iii) Correct Option: (a) 4.47 V
Explanation: Using Einstein’s equation: eVs2 = hc(1/λ2 − 1/λ1) + eVs1. Substituting values for λ1 = 550 nm, λ2 = 190 nm, and Vs1 = 0.19 V gives Vs2 ≈ 4.47 V.
(iv) Correct Option: (b) 2.07 eV
Explanation: Φ = (hc/λ1) − eVs1. Calculating with λ1 = 550 nm and Vs1 = 0.19 V gives Φ ≈ 2.07 eV.
(v) Correct Option: (a) 500 × 1012 Hz
Explanation: f0 = Φ / h. With Φ ≈ 2.07 eV, f0 ≈ 5 × 1014 Hz = 500 × 1012 Hz.
