Question

Determine the wavelength of an electron having kinetic energy of $1.6\times {10}^{-6}erg$.

• A. $12.4cm$
• B. $6.6cm$
• C. $9.6cm$
• D. $4.3cm$

Answer 1

The correct option is A $12.4cm$

Given that, kinetic energy, K.E = $1.6\times {10}^{-6}erg$

1 erg is equal to one gram centimetre-squared per second-squared $(g-c{m}^2/s^2)$.

Also, $E=h\nu =h\frac{c}{\lambda }$ where $\lambda$ = wavelength.

Putting the values in the above equation,

$1.6\times {10}^{-6}=\frac{6.6\times {10}^{-27}\times 3\times {10}^{10}}{\lambda }$

$\therefore \lambda =\frac{6.6\times 3\times {10}^{-17}}{1.6\times \times {10}^{-6}}cm$

$\lambda =12.4cm$.

Hence, option A is correct.