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(C) The Rydberg formula for the wavelength of spectral lines is given by $\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} \right]$.For

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Paschen series

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(C) The Rydberg formula for the wavelength of spectral lines is given by $\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} ight]$.For the upper limit of wavelength,the energy difference between levels must be minimum,which corresponds to the transition from $n_2 = n_1 + 1$ to $n_1$.Substituting the values: $\frac{1}{n_1^2} - \frac{1}{(n_1+1)^2} = \frac{1}{R \lambda}$.Given $\lambda = 18752 \mathring{A} = 18752 	imes 10^{-10} \ m$ and $R = 1.097 	imes 10^7 \ m^{-1}$.$\frac{1}{R \lambda} = \frac{1}{1.097 	imes 10^7 	imes 18752 	imes 10^{-10}} \approx \frac{1}{20570.944} \approx 0.0486$.We know that $\frac{7}{144} \approx 0.0486$. Comparing this to $\frac{1}{n_1^2} - \frac{1}{(n_1+1)^2}$,we set $n_1 = 3$.Thus,$\frac{1}{3^2} - \frac{1}{4^2} = \frac{1}{9} - \frac{1}{16} = \frac{16-9}{144} = \frac{7}{144}$.Since $n_1 = 3$,the series is the Paschen series.

Every series of the hydrogen spectrum has an upper and lower limit in wavelength. The spectral series which has an upper limit of wavelength equal to $18752 \mathring{A}$ is:
(Rydberg constant $R = 1.097 \times 10^7 \ m^{-1}$)

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Every series of the hydrogen spectrum has an upper and lower limit in wavelength. The spectral series which has an upper limit of wavelength equal to $18752 \mathring{A}$ is:(Rydberg constant $R = 1.097 \times 10^7 \ m^{-1}$)