v_1 is the frequency of the series limit of t | vedclass

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(A) For the Lyman series,the frequency is given by $v = RC \left[ \frac{1}{1^2} - \frac{1}{n^2} \right]$,where $n = 2, 3, 4, \dots$For the series limi

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$v_1 - v_2 = v_3$

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(A) For the Lyman series,the frequency is given by $v = RC \left[ \frac{1}{1^2} - \frac{1}{n^2} \right]$,where $n = 2, 3, 4, \dots$For the series limit of the Lyman series,$n = \infty$.Therefore,$v_1 = RC \left[ \frac{1}{1^2} - \frac{1}{\infty^2} \right] = RC$ ..... $(i)$For the first line of the Lyman series,$n = 2$.Therefore,$v_2 = RC \left[ \frac{1}{1^2} - \frac{1}{2^2} \right] = RC \left( 1 - \frac{1}{4} \right) = \frac{3}{4} RC$ ..... $(ii)$For the Balmer series,the frequency is given by $v = RC \left[ \frac{1}{2^2} - \frac{1}{n^2} \right]$,where $n = 3, 4, 5, \dots$For the series limit of the Balmer series,$n = \infty$.Therefore,$v_3 = RC \left[ \frac{1}{2^2} - \frac{1}{\infty^2} \right] = \frac{RC}{4}$ ..... $(iii)$From equations $(i)$,$(ii)$,and $(iii)$,we observe that $v_2 + v_3 = \frac{3}{4} RC + \frac{1}{4} RC = RC = v_1$.Thus,$v_1 = v_2 + v_3$,which implies $v_1 - v_2 = v_3$.

$v_1$ is the frequency of the series limit of the Lyman series,$v_2$ is the frequency of the first line of the Lyman series,and $v_3$ is the frequency of the series limit of the Balmer series. Then:

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