Question

The de broglie wavelength of a neutron with translational kinetic energy 3 kt

Answer 1

Average Kinetic Energy=(3/2)*K*T

Now, use the formula for detailed Broglie Wavelength and substitute the value of K.E= (3/2)*K*T

Note: At atomic level, KE is the average of both Vibrational and Translational KE.

Answer 2

Given that,

Kinetic energy, E = 3 kT

Let us asssumed that, T = 300 K

To find,

The de broglie wavelength of a neutron.

Solution,

The De-Broglie wavelength in terms of kinetic energy is given by :

$\lambda=\dfrac{h}{\sqrt{2mE} }$

Here, E = 3 kT

k is Boltzmann constant

So,

$\lambda=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 1.67\times 10^{-27}\times \dfrac{3}{2}\times 1.8\times 10^{-23}\times 300} }\\\\\lambda=1.27\times 10^{-10}\ m$

or

$\lambda=1.27\ A$

So, the De-Broglie wavelength of the neutron is 1.27 A.

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De-Broglie wavelength

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