NCERT Solutions for Class 12 Physics Chapter 11 - Dual Nature Of Radiation And Matter

1. Photon

A photon is a packet of energy.  It possesses energy given by, E = hν

Where h = 6.62 × 10−34 Js is Plank’s constant and ν is frequency of the photon. 

If λ is wavelength of the photon, then, c = νλ

Here, c = velocity of light.

Therefore, E = hν = hc/λ

Energy of a photon is usually expressed in electron volt (eV). 1eV = 1.6 × 10−19 J

2. Dual Nature of Radiation

The various phenomena concerning radiation can be divided into three parts:

The phenomena such as interference, diffraction, polarization etc. in which interaction of radiation takes places with radiation itself.  Such phenomena can be explained on the basis of electromagnetic (wave) nature of radiation only.

The phenomena such as photoelectric effect, Compton effect, etc. in which interaction of radiation takes place with matter.  Such phenomena can be explained on the basis of quantum (particle) nature of radiation.

The phenomena such as rectilinear propagation, reflection, refraction, etc. in which neither the interaction of radiation takes place with radiation, nor of radiation with matter.  Such phenomena can be explained on the basis of either of the two natures of the radiation.

2.1 De-Broglie Waves

Louis-Broglie put forward a bold hypothesis that matter should also possess dual nature.

The following observations led him to the duality hypothesis for matter.

• The whole energy in this universe is in the form of matter and electromagnetic radiation.

• The nature loves symmetry.  As the radiation has got dual nature, matter should also possess dual nature. 

Thus, according to de-Broglie, a wave is associated with every moving particle. These waves are called de-Broglie waves or matter waves. 

de-Broglie wavelength is given by 

$\lambda = \frac{h}{mv}$

Where h = plank constant

m = mass pf particle

v = speed of particle.

2.2 Conclusion

• Lighter the particle, greater is its de-Broglie wavelength.

• The faster the particle moves, smaller is its de-Broglie wavelength.

• The de-Broglie wavelength of α–particle is independent of the charge or nature of the particle.

• The matter waves are not electromagnetic in nature. If the velocity of the particle is comparable to the velocity of light, then mass of the particle is given by 

$m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$ 

3.  Free Electrons in Metals

Electron is a fundamental constituent of the atom.  A metal contains free electrons, which move about freely through the atomic spaces in a random fashion.  But as soon as an electron leaves the metal, immediately an equal positive charge is produced on the surface of the metal. As a result, the electron is pulled back into the metal and hence remains confined to it. The pull on the electrons at the surface is found to depend on the nature of metal surface and is described by a characteristic of the metal, called work function.

Work Function

The minimum energy, which must be supplied to the electron so that it can just come out of the metal surface is called the work function of the metal.

This process is called electron emission and may be achieved in the following ways

• Thermionic emission. In this process of electron emission, the additional energy is supplied in the form of heat. The emitted electrons are known as thermo-electrons. 

• Photoelectric emission. In this process, as already discussed, the additional energy is supplied by means of electromagnetic radiation. The emitted electrons are known as photoelectrons. 

• Secondary emission, in this process, the fast-moving electrons on collision with the metal surface knock out electrons, called the secondary electrons.

• Field emission. In this process, the electrons are forced out of metal surface by strong electric field

4. Photoelectric Effect

The phenomenon of ejection from a metal surface, when light of sufficiently high frequency falls upon it is known as the photoelectric effect. The electrons so emitted are called photoelectrons.

Experimental Study of Photoelectric Effect:

The apparatus consists of an evacuated glass tube fitted with two electrodes.  The electrode E is called emitting electrode and the other electrode C is called collecting electrode.

When a suitable radiation is incident on the electrode E, electrons are ejected from it.  The electrons, which have sufficient kinetic energy, reach the electrode C despite its negative polarity.  The potential difference between the two electrodes acts as the retarding potential.  As the collecting electrode is made more and more negative, fewer and fewer electrons will reach the cathode and the photo-electric current recorded by the ammeter with fall.  In case, the retarding potential equals V0, called the stopping potential, no electron will reach the cathode and the current will become zero.  In such a case, the work done by stopping potential is equal to the maximum kinetic energy of the electrons i.e.

$eV_0 =\frac{1}{2}\;mv^2_{\text{max}}$

4.1 Laws of Photoelectric Emission

• The emission of photoelectrons takes place only, when the frequency of the incident radiation is above a certain critical value, characteristic of that metal. 

The critical value of frequency is known as the threshold frequency for the metal of the emitting electrode.

• The emission of photoelectrons starts as soon as light falls on metal surface.

• The maximum kinetic energy with which an electron is emitted from a metal surface is independent of the intensity of the light and depends only upon its frequency.

• The number of photoelectrons emitted i.e. photoelectric current is independent of the frequency of the incident light and depends only upon its intensity.

4.2 Einstein's Photoelectric Equation

If a photon of energy hν falls on the surface of a metal and the work function of the metal is hν0

Then $hv = hv_0 + \frac{1}{2}mv^2_{\text{max}}$ . This is Einstein’s photo electric equation. 

Where ν0 = threshold frequency. 

Dual Nature of Radiation and Matter Class 12 NCERT Solutions

This dual nature of matter and radiation class 12 solution is available in PDF format to help CBSE students secure good grades in the board. There is a comprehensive explanation of electricity conduction through gases, electric emission, Hertz observation, Hallwachs’ and Lenard's observation and the practical photoelectric effect. Moreover, concepts like the intensity of light on photocurrent, photoelectric equation of Einstein, photon particle nature of light and wave nature of light has been explained briefly.

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NCERT Solutions for Class 12 Physics Chapter 11

Class 12 physics ch 11 CBSE NCERT Solutions have 37 questions divided as equations and theory. Where the first 19 questions are intext questions while the remaining 18 are additional exercise questions.

Here is a brief description of the questions in the topic dual nature of matter and radiation class 12.

Question 1: Physics class 12 dual nature of matter NCERT solutions.

In the first question, students need to determine the maximum frequency and minimum wavelength of X-rays produced by 30KV electrons.

Question 2: Physics class 12 dual nature of matter NCERT solutions.

Students have to calculate the maximum kinetic energy of emitted electrons, stopping potential and maximum speed emitted by photoelectrons when the work function of caesium metal is 2.14eV and light of frequency is 6 x 10¹⁴ Hz.

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Question 3: NCERT solution of dual nature of radiation and matter.

In the third question, the kinetic energy of photoelectrons emitted, when cutoff photoelectric voltage is 1.5v, needs to be determined.

Question 4:  NCERT solutions of chapter 11 Physics class 12.

This fourth question in dual nature of matter and radiation class 12 asks students to find the energy and momentum of a photon in the light beam and how fast a hydrogen atom travels to have the same speed as a photon. Here, the monochromatic light wavelength is 632.8nm and power emitted is 9.42mW.

Question 5: NCERT solutions for class 12 Physics dual nature.

In the fifth question, students need to calculate how many photons per square meter are incident on the earth per second when the energy flux of sunlight to earth surface is 1.388 x 10³ W/m².

Question 6: Class 12 Physics dual nature of radiation and matter.

This question requires calculating the Planck’s constant where the slope of cut off voltage vs frequency of incident light is 4.12 x 10‾¹⁵ V.

Question 7: NCERT solution of chapter 11 physics class 12.

The seventh question asks students to determine energy per photon associated with the sodium light and the rate at which photons are delivered to the sphere. Here P is 100 W, λ (wavelength) is 589nm.

Question 8: NCERT solutions for class 12 Physics chapter 10 dual nature of radiation and matter.

Question number eight gives the variable that is threshold frequency 3.3 x 10¹⁴ Hz, and light frequency is 8.2 x 10¹⁴ Hz. Here students have to find the cut off voltage for photoelectric emission.

Question 9: NCERT solution of chapter 11 physics class 12.

In this question, students have to find the value of photoelectric emission of metal where the wavelength is 330nm and the work function of the specific metal is 4.2eV.

Question 10: Class 12 Physics Chapter 11.

Here the threshold frequency for photoemission of electrons is needed to be determined. The light of frequency is 7.21 x 10¹⁴ Hz and electrons with a maximum speed of 6.0 x 10⁵ m/s.

Question 11: Dual nature of matter and radiation class 12 NCERT solutions.

This question needs to find the work function of the material from which the emitter is made. Its wavelength is 488nm and stopping potential photoelectrons is 0.38 V.

Question 12 and 13: Chapter 11 Physics class 12 NCERT solutions.

The twelfth question in the topic dual nature of matter and radiation class 12 is how to calculate the momentum when the de Broglie wavelength of electrons is 56 V, and kinetic energy is 120eV.

Question 14: Ch 11 Physics class 12.

In this question, students need to determine the kinetic energy of an electron and whether a de Broglie wavelength will become the neutron. Here λ is 589nm.

Question 15: Class 12 physics ch 11 NCERT solutions.

In this question, students will calculate the de Broglie's wavelength where variables are (a) mass 0.04kg, speed 1.0km/s (b) m 0.06kg and speed 1.0m/s (c) mass 1.0 x 10‾9 kg and speed 2.2 m/s.

Question 16: NCERT solutions for class 12 physics chapter 11.

Here, students will have to determine the momentum of an electron, photon and kinetic energy of an electron.

There are a total of four marks assigned to this topic dual nature of matter and radiation class 12, which is divided as a concise answer and short answer.

Marks Weightage of Dual Nature of Matter and Radiation Class 12 NCERT Solutions

Benefits of Dual Nature of Matter and Radiation Class 12 NCERT Solutions:

• Images and diagrams for step by step explanation.

• Elaborate examples and definition.

• Easy to understand language.

• A brief description of laws by eminent scientists.

Apart from these questions in dual nature of matter and radiation class 12, students have additional exercises to solve which include mathematical and theoretical problems. They should go through the complete chapter thoroughly and understanding it to its fullest.

Important Formulas in NCERT Solutions for Class 12 Physics Chapter 11 - Dual Nature of Radiation and Matter

Here is the list of important formulae that you must remember to solve the numerical problems related to the chapter - Dual Nature of Radiation and Matter.

• Energy of Photon  $\epsilon = hv$

• De Broglie wavelength $\lambda = \dfrac{h}{mv}$

• Photoelectric effect $hv = KE_{\text{max}} + \phi$

• Phase velocity $V_{p} = \dfrac{w}{k}$

We at Vedantu always support your exam preparation. Utilize the link given below to have a specific glance at important formulas in NCERT Solutions for Class 12 Physics Chapter 11 - Dual Nature of Radiation and Matter.

• CBSE Class 12 Physics Formulas for Dual Nature of Radiation and Matter

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NCERT Class 12 Physics Solutions - Free PDF Download

• Chapter 1 - Electric Charges and Fields

• Chapter 2 - Electrostatic Potential and Capacitance

• Chapter 3 - Current Electricity

• Chapter 4 - Moving Charges and Magnetism

• Chapter 5 - Magnetism And Matter

• Chapter 6 - Electromagnetic Induction

• Chapter 7 - Alternating Current

• Chapter 8 - Electromagnetic Waves

• Chapter 9 - Ray Optics and Optical Instruments

• Chapter 10 - Wave Optics

• Chapter 11 - Dual Nature of Radiation and Matter

• Chapter 12 - Atoms

• Chapter 13 - Nuclei

• Chapter 14 - Semiconductor Electronic: Material, Devices And Simple Circuits

• Chapter 15 - Communication Systems