Question

Calculate the de Broglie wavelength for a beam of electron whose energy is $100eV$ :

• A. $1A^0$
• B. $1.23A^0$
• C. $2.46A^0$
• D. None of these

Answer 1

The correct option is B $1.23A^0$

As we know,
E = $\frac{1}{2}$mv${}^2$ = 100 eV = 100 $\times$ 1.6 $\times$ 10${}^{-19}$ J
v${}^2$ = $\frac{2E}{m}$
v = ($\frac{2E}{m}{)}^{1/2)}$
$\lambda$ = $\frac{h}{mv}$ = $\frac{h}{\sqrt{2mE}}$ metre
$\lambda$ = ${\frac{6.6\times {10}^{-34}}{(2\times 9.1\times {10}^{-31}\times 100\times 1.6\times {10}^{-19}}}^{1/2}$
=1.23 $\times$ 10${}^{-10}$ m =$1.23A^0$