Question

an electron of energy 150eV has wavelength of 10^-10 m. The wavelength of a 0.60keV electron is
(a) 0.50 A°. (b) 0.75 A°.
(c) 1.2 A°. (d) 1.5 A°.

Answer 1

Answer : :The wavelength of a 0.60 keV electron is, $\lambda_2=0.5\ \AA$

Explanation

We know that the relation between the wavelength and energy of an electron is

$\lambda=\dfrac{h}{\sqrt{2mE} }$

Where,

E is the energy of an electron.

or

$\lambda \propto\dfrac{1}{\sqrt{E} }$

$\dfrac{\lambda_1}{\lambda_2}=\sqrt{\dfrac{E_2}{E_1}}$........(1)

It is given that,

$\lambda_1=10^{-10}\ m$

$E_1=150\ eV$

$E_2=0.6\ keV=0.6\times 10^3\ ev$

Equation (1) becomes :

$\dfrac{10^{-10}\ m\ }{\lambda_2}=\sqrt{\dfrac{0.6\times 10^3\ eV}{150\ eV}}$

$\lambda_2=0.5\times 10^{-10}\ m$

$\lambda_2=0.5\ \AA$

Hence, the correct option is (a).