Question

Wavelength of a particular transition for $H\, atom$ is $400 \,nm$. What can be the wavelength of $He^+$ for the same transition?

• A. 400 nm
• B. 100 nm
• C. 1600 nm
• D. 200 nm

Answer 1

Answer: (B)

$\frac{1}{\lambda}=R_{H}\left(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}}\right)\times Z^{2}$
$\frac{1}{400}=R_{H}\left(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}}\right)\left(1\right)^{2}\quad\quad\quad\quad\quad ...\left(i\right)$
$\frac{1}{\lambda_{He^{+}}}=R_{H}\left(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{1}}\right)\left(2\right)^{2}\quad \quad \quad\quad ...\left(ii\right)$
On dividing equation (i) by (ii), we get
$\lambda_{He^{+}}=\frac{400}{2^{2}}=\frac{400}{4}=100$ nm