Question

What kinetic energy of a neutron will be associated with de Broglie wavelength?

Answer 1

Step 1. Given data

The wavelength associated with the neutron is $\lambda =1.40\times {10}^{-10}m$

The mass of the neutron is $m_n=1.66\times {10}^{-27}kg$

The value of Planck’s constant is $h=6.6\times {10}^{-34}Js$.

Step 2. Finding relation between energy of a neutron and de Broglie wavelength

The relationship between kinetic energy and velocity $\left(v\right)$ is given by the following equation (1):

$K=\frac{1}{2}{m}_n{v}^2$ …… (1)

The relationship between De Broglie wavelength $\left(\lambda \right)$ and velocity $\left(v\right)$ is given by the following equation (2):

$\lambda =\frac{h}{m_{n}v}$ …… (2)

Using equation (1) and (2), we get,

$K=\frac{h^2}{2{\lambda }^2{m}_n}$

Substituting values in the above equation, we get

$K=\frac{{\left(6.33\times {10}^{-34}\right)}^2}{2\times {\left(1.40\times {10}^{-10}\right)}^2\times 1.66\times {10}^{-27}}$

$K=6.75\times {10}^{-21}J$

Therefore, the kinetic energy of the neutron is $6.75\times {10}^{-21}J$.