Question

compare the wavelength of an electron and a neutron each with kinetic energy of 1meV​

Answer 1

Answer:

Wavelength of an electron is larger than the wavelength of neutron.

Explanation:

We are given that

K.E of an electron=1 Mev=$1.6\times 10^{13} J$

K.E of a neutron=1 Mev=$1.6\times 10^{13} J$

We have to compare between the wavelength of electron neutron

We know that $P=(2mT)^{\frac{1}{2}}$

Where p=Linear momentum

T=Kinetic energy

m= Mass

Mass of an electron=$9.1\times 10^{-31} Kg$

Mass of a neutron=$1.67\times 10^{-27} Kg$

Substitute the values in the given formula

Then, we get

Momentum of an electron=$(2\times 9.1\times 10^{-31}\times 1.6\times 10^{13})^(\frac{1}{2})=5.396\times 10^{-9} Kg m-s$

Wavelength =$\frac{h}{p}$

Wavelength of electron=$\frac{6.626\times 10^{-34}}{5.396\times 01^{-9}}=1.23\times 10^{-25} m$

Momentum of neutron=$(2\times 1.67\times 10^{-27}\times 1.6\times 10^{13})^(\frac{1}{2})=2.31\times 10^{-7} Kg m-s$

Wavelength of neutron=$\frac{6.62\times 10^{-34}}{2.31\times 10^{-7}}=2.86\times 10^{-27} m$

Wavelength of an electron is larger than the wavelength of neutron because mass of an electron is smaller than the mass of neutron.

If Mass is large then wavelength is small and mass is small  then wavelength is large.