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# Solution - Find the De Broglie Wavelength of a Neutron, in Thermal Equilibrium with Matter, Having an Average Kinetic Energy of (3/2) Kt at 300 K. - CBSE (Arts) Class 12 - Physics

ConceptWave Nature of Matter

#### Question

find the de Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) kT at 300 K.

#### Solution

Temperature of the neutron, T = 300 K

Boltzmann constant, k = 1.38 × 10−23 kg m2 s−2 K−1

Average kinetic energy of the neutron:

K' = 3/2 kT

= 3/2 xx 1.38 xx 10^(-23) xx  300 = 6.21 xx 10^(-21) J

The relation for the de Broglie wavelength is given as:

lambda' = h/(sqrt(2K'm_n))

Where

m_n = 1.66 xx 10^(-27) Kg

h = 6.6 xx 10^(-34) Js

K' = 6.75 xx 10^(-21) J

:. lambda' = (6.63 xx 10^(-34))/sqrt(2xx 6.21 xx 10^(-21) xx 1.66 xx 10^(-27)) =  1.46 xx 10^(-10) m = 0.146 nm

Therefore, the de Broglie wavelength of the neutron is 0.146 nm.

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#### APPEARS IN

NCERT Physics Textbook for Class 12 Part 2 (with solutions)
Chapter 11: Dual Nature of Radiation and Matter
Q: 17.2 | Page no. 408

#### Reference Material

Solution for question: Find the De Broglie Wavelength of a Neutron, in Thermal Equilibrium with Matter, Having an Average Kinetic Energy of (3/2) Kt at 300 K. concept: null - Wave Nature of Matter. For the courses CBSE (Arts), CBSE (Commerce), CBSE (Science)
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