Answer:
[tex]\large \boxed{\text{4650 nm}}[/tex]
Explanation:
The second line in the Pfund series corresponds to a transition from n = 7 to n = 5.
To calculate the wavelength of the transition, we can use the Rydberg equation:
[tex]\dfrac{1}{\lambda} = R_{H}\left ( \dfrac{1 }{n_{1}^{2}} - \dfrac{1 }{n_{2}^{2}} \right )[/tex]
where
[tex]R_{H} = 1.097 \times 10^{7} \text{ m}^{-1}[/tex]
If n₁ = 5 and n₂ = 7
[tex]\begin{array}{rcl}\dfrac{1}{\lambda} & = & 1.097 \times 10^{7} \text{ m}^{-1}\left ( \dfrac{1 }{5^{2}} - \dfrac{1 }{7^{2}} \right )\\\\ & = & 1.097 \times 10^{7} \text{ m}^{-1}\left ( \dfrac{1 }{25} - \dfrac{1 }{49} \right )\\\\ & = & 1.097 \times 10^{7} \text{ m}^{-1}\left ( \dfrac{49 - 25 }{49 \times25}\right )\\\\& = & 1.097 \times 10^{7} \text{ m}^{-1}\left ( \dfrac{24 }{1225}\right )\\\\ & = & 2.149 \times 10^{7}\text{ m}^{-1}\\\end{array}\\[/tex]
[tex]\begin{array}{rcl}\lambda & = & \dfrac{1}{2.149 \times 10^{7}\text{ m}^{-1}}\\\\ & = & 4.65 \times 10^{-6} \text{ m}\\ & = & \mathbf{4650} \textbf{ nm}\\\end{array}\\\text{The wavelength of the line is $\large \boxed{\textbf{4650 nm}}$, which is in the $\textbf{infrared region}$}.[/tex]
