In hydrogen spectrum, the shortest wavelength in the Balmer series is $\lambda$. The shortest wavelength in th

Question

In hydrogen spectrum, the shortest wavelength in the Balmer series is $\lambda$. The shortest wavelength in the Bracket series is

Accepted Answer

Shortest wavelength $\frac{1}{\lambda} = R(\frac{1}{n_f^2} - 0)$. For Balmer, $n_f=2$, $\frac{1}{\lambda} = R(\frac{1}{4})$. For Bracket, $n_f=4$, $\frac{1}{\lambda'} = R(\frac{1}{16})$. Thus $\frac{\lambda'}{\lambda} = \frac{16}{4} = 4$, so $\lambda' = 4\lambda$.

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