Question

The wavelength corresponding to maximum energy for hydrogen is $91.2$nm. Find the corresponding wavelength for $H{e}^{+}$ ion.

• A. $2.28$nm
• B. $22.8$ nm
• C. $182.4$ nm
• D. $364.8$ nm

Answer 1

Answer: (A)

$2.28$nm

For maximum energy, $n1=1$ and $n_2=$ infinite

$1/\lambda =R_H(1/n_1^2-1/n_2^2)Z^2$

Since $R_H$ is a constant and transition remains the same

$1/\lambda$ is directly proportional to $Z^2$

${\lambda }_{He}/{\lambda }_H=\frac{2_H^2}{2_{He}^2}=1/4$

Hence, ${\lambda }_{He}=1/4\times 91.2=22.8nm$