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# Obtain the De Broglie Wavelength Associated with Thermal Neutrons at Room Temperature (27 ºC). Hence Explain Why a Fast Neutron Beam Needs to Be Thermalised with the Environment before It Can Be Used for Neutron Diffraction Experiments. - CBSE (Science) Class 12 - Physics

#### Question

Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27 ºC). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

#### Solution

De Broglie wavelength = 1.447 xx 10^(-10) m

Room temperature, T = 27°C = 27 + 273 = 300 K

The average kinetic energy of the neutron is given as:

E = 3/2 kT

Where,

k = Boltzmann constant = 1.38 × 10−23 J mol−1 K−1

The wavelength of the neutron is given as:

lambda = h/sqrt(2m_n E) = h/(sqrt(3m_n KT))

= (6.6 xx 10^(-34))/sqrt(3xx1.675 xx 10^(-27) xx 1.38 xx 10^(-23) xx 300)

= 1.447 xx 10^(-10) m

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.

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#### APPEARS IN

NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 11: Dual Nature of Radiation and Matter
Q: 32.2 | Page no. 410

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Solution Obtain the De Broglie Wavelength Associated with Thermal Neutrons at Room Temperature (27 ºC). Hence Explain Why a Fast Neutron Beam Needs to Be Thermalised with the Environment before It Can Be Used for Neutron Diffraction Experiments. Concept: Wave Nature of Matter.
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