Question

if the mass of neutron is 1.7*10^-27kg then the de- broglie wavelength of neutron of energy 3ev is

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Answer 1

Answer:

The relationship between the wavelength and the mass of a particle is

\displaystyle\lambda = \frac{h}{p}\,=\frac{h} {\sqrt{2 m K}}λ=

ph = 2mKh

Thus, for same K, the wavelength is inversely proportional to the square root of mass as 1/\sqrt{m}1/ m.

Now, (\dfrac {m_n}{m_e})=( memn )= 1838.6, therefore for the same energy(150eV)

(a) Wavelength of neutron =1/\sqrt{1838.6}\,\times 10^{-10}m = 2.33\times 10^{-12}m1/ 1838.6 ×10 −10 m=2.33×10 −12 m.

The interatomic spacing is about a hundred times greater. A neutron beam of 150 eV energy is therefore not suitable for diffraction experiments.

(b) \displaystyle\lambda = 1.45 \times 10^{-10} m [use \displaystyle\lambda = [h/\sqrt{3 m k T}]λ=1.45×10 −10 m[use λ=[h/

3m k T ] which is comparable to interatomic spacing in a crystal.

Clearly, from (a) and (b) above, thermal neutrons are a suitable probe for diffraction experiments, so a high energy neutron beam should be first thermalised before using it for diffraction

Explanation:

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