Physics - Modern Physics Question with Solution | TestHub

In any spectral series of the hydrogen atom, the transition occurs from a higher energy level $n_2$ to a lower energy level $n_1$.

The energy difference between the levels is given by $\Delta E=E_{n_2}-E_{n_1}=\frac{hc}{\lambda }$.

For the first line of the series, the transition is from the immediately next higher level, i.e., $n_2=n_1+1$. This transition involves the minimum energy difference ($\Delta E_{\text{min}}$). Since wavelength is inversely proportional to energy ($\lambda \propto \frac{1}{\Delta E}$), the first line has the longest wavelength.

For the series limit, the transition is from $n_2=\infty$ to $n_1$. This transition involves the maximum energy difference ($\Delta E_{\text{max}}$). Therefore, the series limit corresponds to the shortest wavelength.

Thus, the wavelength of the first line is the longest and the series limit is the shortest.

Answer: longest and shortest