The wavelength is given by
\[ \lambda_0 = R_H(\frac{1}{n_1^2}- \frac{1}{n_2^2}) ,\]
where $R_H$ is constant $1.0968e^7$ per meter, and $n_1,n_2$ are integers corresponfing to the principal quantum numbers involved in the transition with $n_2>n_1$.
The red $H\alpha$ line is resulted from the electron transition from $n_2=3$ to $n_1=2$ energy level.
Some of the neutral hydrogen atoms entering the shock are occasionally excited and emit narrow Blamer lines, whose width is related to the kinetic temperature of the upstream neutrals;
part of the original neutrals undergo instead a charge-exchange process, and then the new fast moving neutrals (formerly being shocked ions) will emit broad Balmer lines; these second-generation neutrals have some change to undergo charge exchange again and so to create further generations of neutrals, until all neutrals will eventually get ionized. Due to this chain of processes, Balmer lines are expected to show a broad and narrow component.
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