An orbital electron in the ground state of hydrogen has the magnetic moment 𝜇. This orbital electron is excited to 3^rd excited state by some energy transfer to the hydrogen atom. The new magnetic moment of the electron is 𝑛𝜇. The value of 𝑛 is _____.

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answer is 4.

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Detailed Solution

Magnetic moment of an electron in the nth orbital is given by $μ$ =iA
$\begin{array}{l} \Rightarrow μ = \frac{ev}{2 {πr}_{n}} \times {πr}_{n}^{2} \Rightarrow μ \propto {vr}_{n} \Rightarrow μ \propto \frac{1}{n} \times n^{2} \Rightarrow μ \propto n \\ \Rightarrow \frac{μ_{2}}{μ_{1}} = \frac{n_{2}}{n_{1}} \Rightarrow \frac{μ_{2}}{μ} = \frac{4}{1} \Rightarrow μ_{2} = 4 μ (3^{rd} excited state \Rightarrow n = 4) \end{array}$