Question

The wavelengths of electron waves in two orbits is $3:5$ . The ratio of kinetic energy of electrons will be

• A. 25 : 9
• B. 5 : 3
• C. 9 : 25
• D. 3 : 5

Answer 1

Answer: (A)

According to de-Broglie's equation.
$\lambda =\frac{h}{mv}$
$\Rightarrow {\lambda }^2=\frac{h^2}{m^2{v}^2}$
or $m{v}^2=\frac{h^2}{m{\lambda }^2}$
$\because KE(K)=\frac{1}{2}m{v}^2$
$\therefore KE(K)=\frac{1}{2}\frac{h^2}{m{\lambda }^2}$
$\Rightarrow \frac{K_1}{K_2}={\left(\frac{{\lambda }_2}{{\lambda }_2}\right)}^2={\left(\frac{5}{3}\right)}^2$
$\therefore K_1:K_2=25:9$