Reduced mass of atomic hydrogen:

The hydrogen atom consists of a proton and an electron.

Let us consider \( m_1 \) be the mass of the proton and \( m_2 \) be the mass of the electron. So the reduced mass will be,

\( \displaystyle{\mu=\frac{m_1m_2}{m_1+m_2}} \)

or, \( \displaystyle{\mu=\frac{m_2}{1+\frac{m_2}{m_1}}} \)

or, \( \displaystyle{\mu=m_2{\left(1+\frac{m_2}{m_1}\right)}^{-1}} \)

or, \( \displaystyle{\mu=m_2\left(1-\frac{m_2}{m_1}\right)} \) (using binomial theorem)

or, \( \mu=m_2 \)

[since, \( \frac{m_2}{m_1}=\frac{1}{183} \), then \( m_2<<m_1 \)]

So the reduced mass ( \( \mu \)) of the atomic hydrogen is approximately equal to the mass of the electron ( \( m_2 \)).