If the series limit frequency of the Balmer s | vedclass

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Question

(C) The frequency $
u$ of emitted radiation for a transition in a hydrogen atom is given by $
u = cR \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} ight

Vedclass · Accepted Answer

$\frac{
u_{B}}{4}$

Vedclass · Answer

(C) The frequency $
u$ of emitted radiation for a transition in a hydrogen atom is given by $
u = cR \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} ight]$.For the series limit,the transition occurs from $n_2 = \infty$ to $n_1$.For the Balmer series,$n_1 = 2$,so $
u_{B} = cR \left[ \frac{1}{2^2} - \frac{1}{\infty^2} ight] = \frac{cR}{4}$.For the Brackett series,$n_1 = 4$,so $
u' = cR \left[ \frac{1}{4^2} - \frac{1}{\infty^2} ight] = \frac{cR}{16}$.Dividing the two expressions: $\frac{
u'}{
u_{B}} = \frac{cR/16}{cR/4} = \frac{4}{16} = \frac{1}{4}$.Therefore,$
u' = \frac{
u_{B}}{4}$.

If the series limit frequency of the Balmer series is $\nu_{B}$,then the series limit frequency of the Brackett series is

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