Question

The wavelength photon obtained by electron transition between two level in H-atom and singly ionised $He$ are ${\lambda }_1$ and ${\lambda }_2$ respectively, then:

• A. ${\lambda }_2={\lambda }_1$
• B. ${\lambda }_2=2{\lambda }_1$
• C. ${\lambda }_2={\lambda }_1/2$
• D. ${\lambda }_2={\lambda }_1/4$

Answer 1

The correct option is D ${\lambda }_2={\lambda }_1/4$

$E_n=\frac{E_1}{n^2}$

For hydrogen like species,

$E_n=E_1\times \frac{Z^2}{n^2}$

$E_n=\frac{hc}{\lambda }$

$E_n$ is directly proportional to $Z^2$ and inversely proportional to $\lambda$.

$\frac{E_{H_2}}{E_{He}}=\frac{Z_{H_2}^2}{Z_{He}^2}=\frac{{\lambda }_2}{{\lambda }_1}$

$\frac{{\lambda }_2}{{\lambda }_1}=\frac{1}{4}$

$\Rightarrow {\lambda }_2=\frac{{\lambda }_1}{4}$