The frequencies for the series limit of the B | vedclass

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(A) The frequency of a spectral line is given by $f = Rc \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$.For the series limit of the Balmer series $

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$f_1-f_2=f_3$

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(A) The frequency of a spectral line is given by $f = Rc \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$.For the series limit of the Balmer series $(n_1=2, n_2=\infty)$: $f_1 = Rc \left( \frac{1}{2^2} - 0 \right) = \frac{Rc}{4}$.For the series limit of the Paschen series $(n_1=3, n_2=\infty)$: $f_3 = Rc \left( \frac{1}{3^2} - 0 \right) = \frac{Rc}{9}$.For the first line of the Balmer series $(n_1=2, n_2=3)$: $f_2 = Rc \left( \frac{1}{2^2} - \frac{1}{3^2} \right) = Rc \left( \frac{1}{4} - \frac{1}{9} \right)$.Substituting the expressions for $f_1$ and $f_3$ into the equation for $f_2$:$f_2 = \frac{Rc}{4} - \frac{Rc}{9} = f_1 - f_3$.Rearranging the terms,we get $f_1 - f_2 = f_3$.

The frequencies for the series limit of the Balmer and Paschen series are $f_1$ and $f_3$,respectively. If the frequency of the first line of the Balmer series is $f_2$,then the relation between $f_1, f_2$,and $f_3$ is:

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