Question

Calculate the velocity of a neutron needed to achieve a wavelength of 1.40 å . (take the mass of the neutron m=1.6749×10−27kg).

Answer 1

The answer to the question is $2.827\times 10^3\ m/s$i.e the velocity required to achieve that desired wavelength is  $2.827\times 10^3\ m/s$

CALCULATION:

From de Broglie theory, we know that a moving microscopic particle is associated with a wave. The wavelength of the particle moving with velocity v is calculated as-

                                        $\lambda=\frac{h}{mv}$

Here, m is the mass of the particle and h is the Plack's constant.

We have been given wavelength $\lambda=1.40\ A^{0}$

                                                                $=\ 1.40\times 10^-10\ m$

The mass of the neutron m = $1.6749\times 10^-27\ kg$

Hence, the velocity required to achieve that wavelength is calculated as-

                                         $v=\ \frac{h}{m\lambda}$

                                                $=\frac{6.63\times 10^-34}{1.6749\times 10^-27\times 1.40\times 10^-10}\ m/s$

                                                $=2.827\times 10^3\ m/s$      [ans]

Answer 2

Given:

Wavelength = 1.40 * 10^-10

Mass of the neutron = 1.6749 * 10^−27 kg

To find:

The velocity of the neutron

Solution:

By De broglie's law,

λ = h / mv

Where,

λ - Wavelength of the particle

m - Mass of the particle

h - Plack's constant ( 6.63 * 10^-34 )

Substituting the values,

1.40 * 10^-10 = 6.63 * 10^-34 / ( 1.6749 * 10^-27 ) * v

v =  6.63 * 10^-34 / ( 1.6749 * 10^-27 ) * 1.40 * 10^-10

Hence,

v = 2.827 * 10^3 m/s

The velocity of a neutron needed to achieve a wavelength of 1.40 å is 2.827 * 10^3 m/s.