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Chapter 4: Q20E (page 134)

What is the wavelength of a neutron of kinetic energy 1MeV? Of kinetic energy20eV? (The difference is important for the fission of uranium, as a neutron will be more easily absorbed when its wavelength is very large compared with the dimensions of the wavelength behaves more like a diffuse wave than like a localized particle)

Short Answer

Expert verified

The wavelength of Neutron of kinetic energy

λ1MeV=2.87×10-14 m

λ20eV=6.41×10-12 m

Step by step solution

01

Step 1:Given data.

Given that the neutron's K.E. is 1 MeVand20 eV

02

Wavelength of the neutron with the known kinetic energy

KE=p22mKE=h2/λ22mλ=h2m×KE

03

Wavelength for the Kinetic Energy of20 eV .

KE=20 eV=32×10-19 J

λ=6.63×10-34 J⋅s2×(1.67×10-27 kg)×(32×10-19 J)=6.41×10-12m

Therefore, the wavelength of Neutron of kinetic energy

(a)λ1MeV=2.87×10-14 m

(b)λ20eV=6.41×10-12 m

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