What is the exact mathematical expression for the wavelength of the third spectral line of the Balme — Atomic Structure Chemistry Question

💡 Solution & Explanation

For the Balmer series, $n_1 = 2$. The spectral lines sequentially correspond to $n_2 = 3$ ($1^{st}$ line), $n_2 = 4$ ($2^{nd}$ line), and $n_2 = 5$ ($3^{rd}$ line). Applying the Rydberg formula: $\frac{1}{\lambda} = R_H (\frac{1}{2^2} - \frac{1}{5^2}) = R_H (\frac{1}{4} - \frac{1}{25}) = R_H (\frac{25 - 4}{100}) = \frac{21 R_H}{100}$. Therefore, the wavelength $\lambda = \frac{100}{21 R_H}$.