The frequency of the first line of the Pasche | vedclass

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Question

(A) The frequency of a spectral line is given by the formula: $v = RC Z^{2} \left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right)$.For the Paschen

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$\frac{7RC}{9}$

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(A) The frequency of a spectral line is given by the formula: $v = RC Z^{2} \left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} ight)$.For the Paschen series,the transition is to the $n_{1} = 3$ energy level. The first line corresponds to the transition from $n_{2} = 4$ to $n_{1} = 3$.For the $Be^{+3}$ ion,the atomic number $Z = 4$. Substituting these values into the formula:$v = RC 	imes (4)^{2} 	imes \left( \frac{1}{3^{2}} - \frac{1}{4^{2}} ight)$$v = RC 	imes 16 	imes \left( \frac{1}{9} - \frac{1}{16} ight)$$v = 16 RC 	imes \left( \frac{16 - 9}{144} ight)$$v = 16 RC 	imes \frac{7}{144}$$v = \frac{7 RC}{9}$

The frequency of the first line of the Paschen series in the spectrum of the $Be^{+3}$ ion is:

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