Hydrogen \((_1H^1),\) Deuterium \((_1H^2)\),singly ionised Helium \((_2He^4)^+\) and doubly ionised lithium \({\left( {{}_3^6Li} \right)^{ + + }}\), all have one electron around the nucleus. Consider an electron transition from \(n = 2\) to \(n = 1\). If the wavelengths of emitted radiation are \(λ_1,λ_2,λ_3\) and \(λ_4\) respectively then approximately which one of the following is correct?

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Answer & Solution

Correct Answer

(B) \(λ_1 =λ_2 =4λ_3 =9λ_4\)

Step-by-step Solution

Detailed explanation

Wave number \(\frac{1}{\lambda}=R Z^{2}\left[\frac{1}{n_{1}^{2}}-\frac{1}{n^{2}}\right]\)

\(\Rightarrow \quad \lambda \propto \frac{1}{Z^{2}}\)

By question \(n=1\) and \(n_{1}=2\)

Then, \(\lambda_{1}=\lambda_{2}=4 \lambda_{3}=9 \lambda_{4}\)

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