Physics Class 12 NCERT Solutions: Chapter 11 Dual Nature of Radiation and Matter Part 15 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Photons and Energy Levels

Q: 32. (A) Obtain the de Broglie wavelength of a neutron of kinetic energy . As you have seen in Exercise 31 (Reference: Chapter11 Dual Nature of Radiation and Matter Part 14) , an electron beam of same energy be equally suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain.

(B) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature . Hence explain why a fast neutron beam needs to be the rmalised with the environment before it can be used for neutron diffraction experiments.

Answer:

(A) De Broglie wavelength ; neutron is not suitable for the diffraction experiment

Kinetic energy of the neutron,

Mass of a neutron,

The kinetic energy of the neutron is given by the relation:

Where, Velocity of the neutron

Momentum of the neutron

De-Broglie wavelength of the neutron is given as:

It is clear that wavelength is inversely proportional to the square root of mass.

Hence, wavelength decreases with increase in mass and vice versa.

It is given in the previous problem that the inter-atomic spacing of a crystal is about , i.e.. , . Hence, the inter-atomic spacing is about a hundred times greater. Hence, a neutron beam of energy is not suitable for diffraction experiments.

(B) De Broglie wavelength

Room temperature,

The average kinetic energy of the neutron is given as:

Where,

Boltzmann constant

The wavelength of the neutron is given as:

This wavelength is comparable to the inter-atomic spacing of a crystal. Hence, the high-energy neutron beam should first be thermalised, before using it for diffraction.

Q: 33. An electron microscope uses electrons accelerated by a voltage of . Determine the de Broglie wavelength associated with the electrons. If other factors (such as numerical aperture, etc.) are taken to be roughly the same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses yellow light?

Answer:

Electrons are accelerated by a voltage,

Charge on an electron,

Mass of an electron,

Wavelength of yellow light

The kinetic energy of the electron is given as:

De Broglie wavelength is given by the relation:

This wavelength is nearly times less than the wavelength of yellow light.

The resolving power of a microscope is inversely proportional to the wavelength of light used. Thus, the resolving power of an electron microscope is nearly times that of an optical microscope.