Question

Calculate the debroglie wavelength of neutron energy 28.8ev

Answer 1

Explanation:

first of all energy =1/2 mv^2, where m= mass of neutron

1ev = 1.6×10^-19 j

find velocity v

then de broglie wavelength lemda=h/mv

h= plank's constant =6.626×10^-34

m= mass of neutron=1.67×10^-27kg

v= velocity (m/s)find the above energy equation .

Answer 2

Given:

• The kinetic energy of neutron = 28.8 ev

To Find:

• The de Broglie wavelength of the neutron.

Solution:

First, let us convert the unit of kinetic energy into Joules.

K = 28.8 ev = 28.8 × 1.6 × $10^{-19}$ = 46.08 × $10^{-19}$  J { 1 ev = 1.6 × $10^{-19}$}

The formula to find the de Broglie wavelength is given by,

λ = h/√(2Km) →  {equation 1}

Where "λ" is the de Broglie wavelength, "h" is the Planck's constant( h = 6.6 × $10^{-34}$ $m^2$ Kg/s), "K" is the kinetic energy of the neutron, and "m" is the mass of the neutron(1.6 × $10^{-27}$ Kg)

On substituting the values in equation 1 we get,

⇒ λ = 6.6 × $10^{-34}$/√(2×1.6 × $10^{-27}$ × 46.08 × $10^{-19}$)  { multiplying the values in denominator}

⇒ λ = 6.6 × $10^{-34}$/√147.456 × $10^{-46}$  {dividing the values}

⇒ λ = 0.545 × $10^{-12}$ m

∴ The de Broglie wavelength of neutron = 0.545 × $10^{-12}$