What is the maximum wavelength of the H_{alph | vedclass

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(A) The Balmer series corresponds to transitions where the electron jumps to the $n_f = 2$ energy level from higher levels $n_i = 3, 4, 5, \dots$.The

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$656.3$

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(A) The Balmer series corresponds to transitions where the electron jumps to the $n_f = 2$ energy level from higher levels $n_i = 3, 4, 5, \dots$.The wavelength $\lambda$ is given by the Rydberg formula: $\frac{1}{\lambda} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} ight)$,where $R \approx 1.097 	imes 10^7 \ m^{-1}$.The $H_{\alpha}$ line corresponds to the transition from $n_i = 3$ to $n_f = 2$.Substituting the values: $\frac{1}{\lambda} = 1.097 	imes 10^7 \left( \frac{1}{2^2} - \frac{1}{3^2} ight) = 1.097 	imes 10^7 \left( \frac{1}{4} - \frac{1}{9} ight) = 1.097 	imes 10^7 \left( \frac{5}{36} ight)$.$\frac{1}{\lambda} \approx 1.5236 	imes 10^6 \ m^{-1}$.$\lambda \approx 6.563 	imes 10^{-7} \ m = 656.3 \ nm$.

What is the maximum wavelength of the $H_{\alpha}$ line in the Balmer series of the hydrogen atom (in $nm$)?

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