CBSE Class 12 Physics Exemplar NCERT Solutions Chapter 11: Dual Nature of Radiation and Matter
CBSE Class 12 Physics chapter on the Dual Nature of Radiation and Matter explores the fascinating interplay between waves and particles. This section delves into critical concepts like the de-Broglie wavelength, which describes the wave-like properties of matter, and the energy of photons, particularly in the context of overcoming nuclear binding energy. The chapter also examines electron emission from metal surfaces, a phenomenon explained by the photoelectric effect. A cornerstone of this topic is the Davisson-Germer experiment, which provided crucial experimental validation for the wave nature of electrons. The NCERT Solutions for this chapter offer detailed, step-by-step explanations, simplifying complex theories and problem-solving approaches. These resources are invaluable for students aiming to solidify their understanding of modern physics principles and excel in their examinations.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 12 |
| Subject | Physics Exemplar |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 11 |
Chapter summary
Chapter 11, 'Dual Nature of Radiation and Matter,' explores the wave-particle duality of light and matter. The NCERT Solutions focus on understanding de-Broglie wavelength, photon energy calculations for nuclear interactions, and the photoelectric effect principles related to electron emission. It also includes explanations of experimental verification like the Davisson-Germer experiment. These solutions provide clear, step-by-step problem-solving approaches for the exercises.
Learning outcomes
- Understand the relationship between a particle's momentum and its de-Broglie wavelength.
- Calculate the de-Broglie wavelength of a particle based on its kinetic energy or velocity.
- Determine the energy of a photon required to overcome nuclear binding energy.
- Explain the conditions for electron emission from a metal surface when bombarded by an electron beam.
- Analyze the Davisson-Germer experiment and its significance in confirming the wave nature of electrons.
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Questions and Solutions
Dual Nature of Radiation
and Matter
Multiple Choice Questions (MCQs)
<math>\boxtimes_{\boldsymbol{i}}</math> 1 A particle is dropped from a height H. The de-Broglie wavelength of the
particle as a function of height is proportional to
(b) <math>H^{1/2}</math>
(d) <math>H^{-1/2}</math>
(c) <math>H^0</math>
(a) H
K Thinking Process
The de-broglie wavelength <math>\lambda</math> is given by <math>\lambda = \frac{h}{n}</math>. mv Ans. (d) Velocity of a body falling from a height H is given by
<math>V = \sqrt{2gH}</math>
We know that de-broglie wavelength
<math>\lambda = \frac{h}{mv} = \frac{h}{m\sqrt{2gH}} \Rightarrow \frac{h}{m\sqrt{2g}\sqrt{H}}</math>
Here, <math>\frac{h}{m\sqrt{2\alpha}}</math> is a constant <math>\phi</math> say 'K'.
<math>\lambda = K \frac{1}{\sqrt{H}} \Rightarrow \lambda \propto \frac{1}{\sqrt{H}}</math> So, <math>\lambda \propto H^{-1/2}</math>
<math>\Rightarrow</math>
<math>\boxtimes_{\boldsymbol{.}}</math> <math>\boxtimes_{\boldsymbol{.}}</math> The wavelength of a photon needed to remove a proton from a nucleus
which is bound to the nucleus with 1 MeV energy is nearly
(b) <math>1.2 \times 10^{-3}</math> nm
(a) 1.2 nm
(c) <math>1.2 \times 10^{-6}</math> nm
(d) <math>1.2 \times 10 \text{ nm}</math>
K Thinking Process
Energy of a photon is <math>E = \frac{hc}{\lambda}</math>, where <math>\lambda</math> is the minimum wavelength of the photon required
to eject the proton from nucleus.
Ans. (b) Given in the question,
Energy of a photon, <math>E = 1 \,\text{MeV} \implies = 10^6 \,\text{eV}</math>
Now, <math>hc = 1240 \, \text{eVnm}</math> Now, <math>E = \frac{hc}{\lambda}</math>
<math>\Rightarrow</math> <math>l = \frac{hc}{E} = \frac{1240 \text{ eVnm}}{10^6 \text{ eV}}</math>
<math>= 1.24 \times 10^{-3} \text{ nm}</math>
<math>\bigcirc</math> 3 Consider a beam of electrons (each electron with energy <math>E_0</math>) incident on a metal surface kept in an evacuated chamber. Then,
- no electrons will be emitted as only photons can emit electrons
- electrons can be emitted but all with an energy, <math>E_0</math>
- electrons can be emitted with any energy, with a maximum of <math>E_0 - \phi</math> (φ is the work function)
- electrons can be emitted with any energy, with a maximum of <math>E_0</math>
Ans. (d) When a beam of electrons of energy <math>E_0</math> is incident on a metal surface kept in an evacuated chamber electrons can be emitted with maximum energy <math>E_0</math> (due to elastic collision) and with any energy less than <math>E_0</math>, when part of incident energy of electron is used in liberating the electrons from the surface of metal.
<math>\boxtimes</math>. 4 Consider figure given below. Suppose the voltage applied to A is increased. The diffracted beam will have the maximum at a value of <math>\theta</math> that
- will be larger than the earlier value (b) will be the same as the earlier value
- will be less than the earlier value (d) will depend on the target
Nickel
Electron beam Α target
Electron - LT gun
Diffracted Vacuum
electron chamber
Movable beam
collector
To galvanometer
K Thinking Process
The figure given here shows the Davisson-Germer experiment which was held to verify the wave nature of electrons.
Common mistakes
- Incorrectly applying the de-Broglie wavelength formula to photons instead of particles with mass.
- Errors in unit conversions, especially between eV, MeV, Joules, and nanometers.
- Confusing the maximum kinetic energy of emitted electrons with the incident electron energy in electron-metal interactions.
- Misinterpreting the relationship between applied voltage and the diffraction angle in experiments like Davisson-Germer.
Revision tips
- Focus on the de-Broglie wavelength formula and its application to different scenarios.
- Practice problems involving photon energy and its relation to wavelength, especially for nuclear processes.
- Review the conditions and outcomes of the photoelectric effect and electron emission experiments.
- Understand the significance of the Davisson-Germer experiment as evidence for wave-particle duality.
Practice MCQs
Q1. A particle is dropped from a height H. How is its de-Broglie wavelength related to the height?
Explanation: The velocity of a falling particle is given by (2gH). The de-Broglie wavelength is lambd/(mv). Substituting V, we get lambd/(m*sqrt(2gH)), which shows lambda is proportional to H^(-1/2).
Q2. What is the approximate wavelength of a photon needed to remove a proton from a nucleus bound by 1 MeV energy?
Explanation: The energy of the photon must be at least equal to the binding energy, = 10^6 eV. Using /lambda and h, we find lambd// 10^6 e
Q3. When a beam of electrons with energy E0 is incident on a metal surface in a vacuum, what can be the energy of the emitted electrons?
Explanation: Electrons can be emitted with energies less than E0. The maximum energy an emitted electron can have is E0, which occurs in elastic collisions where no energy is lost to the metal. Some energy might be lost in inelastic collisions or to overcome the work function.
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