According to the Rydberg equation, the longest wavelength (in nm) in the series of H-atom lines with n₁ = 3 is A)1875 nm. B)1458 nm. C)820. nm. D)656 nm. E)365 nm.

Question

Quizplus · Accepted Answer

The Rydberg equation for the wavelength ($\lambda$) of light emitted when an electron transitions between energy levels in a hydrogen atom is given by $\frac{1}{\lambda} = R_H \left( \frac{1}{n_{\text{lower}}^2} - \frac{1}{n_{\text{upper}}^2} \right)$, where $R_H$ is the Rydberg constant ($1.097 \times 10^7 \text{ m}^{-1}$), $n_{\text{lower}}$ is the principal quantum number of the lower energy level, and $n_{\text{upper}}$ is the principal quantum number of the higher energy level. For the longest wavelength, we want the smallest energy difference, which occurs for a transition from $n = 4$ to $n = 3$. Plugging these values into the Rydberg formula and solving for $\lambda$ gives the longest wavelength in the series. Calculating this yields a wavelength of approximately 1875 nm, making option A correct.

According to the Rydberg Equation, the Longest Wavelength (In Nm)