Question

Similar to electron diffraction, a neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with the neutron.

Answer 1

Hint: There is a relationship between wavelength and velocity of the neutron.
As per de-Broglie equation the relationship is as follows.
\[\lambda =\dfrac{h}{m\times v}\text{ (}or)\text{ }v=\dfrac{h}{m\times v}\]
Where h = Planck’s constant
 m = mass of the neutron
v = Velocity of the neutron
$\lambda $ = Wavelength of the neutron.

Complete step by step answer:
- In the question it is given that in a neutron diffraction microscope the wavelength used is 800 pm, and we have to calculate the characteristic velocity associated with the neutron.
- From the de-Broglie equation we can calculate the velocity of the neutron by using the wavelength of the neutron and it is as follows.
\[v=\dfrac{h}{m\times v}\]
Where h = Planck’s constant = $6.626\times {{10}^{-34}}$
 m = mass of the neutron = $1.675\times {{10}^{-27}}Kg$
v = Velocity of the neutron
$\lambda $ = Wavelength of the neutron = 800 pm = $800\times {{10}^{-12}}m$

- Substitute all the known values in the above de-Broglie equation to get the velocity of the photon associated with the 800 pm wavelength.
\[\begin{align}
  & v=\dfrac{h}{m\times v} \\
 & v=\dfrac{6.626\times {{10}^{-34}}}{(1.675\times {{10}^{-27}})(800\times {{10}^{-12}})} \\
 & v=4.94\times {{10}^{4}}m/\sec \\
\end{align}\]

- The velocity of the photon associated with the 800 pm wavelength in a neutron diffraction microscope is $4.94\times {{10}^{4}}m/\sec $ .

Note: Neutron diffraction is used to conclude the static structure for gases and amorphous solids. Maximum experiments aim to find the structure of crystalline solids using neutron diffraction microscopy in crystallography. Neutron diffraction microscope and electron diffraction are closely related to X-ray diffraction studies.