Question

The wave number of a particular spectral line in the atomic spectrum of a hydrogen like species increases $9/4$ times when deuterium nucleus is introduced into its nucleus, then which of the following will be the initial hydrogen like species?

• A. ${Li}^{2+}$
• B. ${Li}^{+}$
• C. ${He}^{+}$
• D. ${Be}^{3+}$

Answer 1

The correct option is D ${Be}^{3+}$

For hydrogen-like atoms spectra,

$\lambda \propto \frac{n^2}{Z}$

where,

$\lambda =$wavelength

$n=$ The number which element excited

$Z=$Atomic number

Given that for hydrogen

$\frac{n^2}{Z}=\frac{9}{8}$

check which ion's $\lambda \propto \frac{9}{8}$

$A)$ for $L{i}^{+2}$

$\lambda \propto \frac{n^2}{Z}\Rightarrow \lambda \propto \frac{2^2}{3}=\frac{4}{3}$

$B)$ for $L{i}^{+}$

$\lambda \propto \frac{n^2}{Z}\Rightarrow \lambda \propto \frac{1^2}{3}=\frac{1}{3}$

$c)$ for $H{e}^{+}$

$\lambda \propto \frac{n^2}{Z}\Rightarrow \lambda \propto \frac{1^2}{2}=\frac{1}{2}$

$c)$ for $B{e}^{3+}$

$\lambda \propto \frac{n^2}{Z}\Rightarrow \lambda \propto \frac{3^2}{4}=\frac{9}{4}$

$Hencethecorrectanswerisoption\left(D\right).$