Question

If ${\lambda }_1$ and ${\lambda }_2$ denote the wavelength of de Broglie waves for electrons in Bohr’s first and second orbits in the hydrogen atom, then $\frac{{\lambda }_1}{{\lambda }_2}$ will be:

• A. $2$
• B. $\frac{1}{2}$
• C. $4$
• D. $\frac{1}{4}$

Answer 1

The correct option is B

$\frac{1}{2}$

$\lambda =\frac{h}{\sqrt{2Em}}$ or $\lambda \propto \frac{1}{\sqrt{E}}$
$\frac{{\lambda }_1}{{\lambda }_2}=\sqrt{\frac{E_2}{E_1}}=\sqrt{\frac{3.4}{13.6}}=\frac{1}{2}$