Question

Wavelength of a particular transition for $Hatom$ is $400nm$. What can be the wavelength of $H{e}^{+}$ for the same transition?

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

Answer 1

Answer: (B)

$\frac{1}{\lambda }=R_H\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)\times Z^2$
$\frac{1}{400}=R_H\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right){\left(1\right)}^2...\left(i\right)$
$\frac{1}{{\lambda }_{H{e}^{+}}}=R_H\left(\frac{1}{n_1^2}-\frac{1}{n_1^2}\right){\left(2\right)}^2...\left(ii\right)$
On dividing equation (i) by (ii), we get
${\lambda }_{H{e}^{+}}=\frac{400}{2^2}=\frac{400}{4}=100$ nm