If Rydberg's constant is R , the longest wavelength of radiation in Paschen series will be 7 R α , where α = ______.

Question

If Rydberg's constant is R , the longest wavelength of radiation in Paschen series will be 7 R α ​ , where α = ______.

TestHub · Accepted Answer

In the Paschen radiation series, the longest wavelength corresponds to the transition between $n = 3$ and $n = 4$ . The formula for the wavelength in the given transition can be written as,

$\frac{1}{λ} = R Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}}) ... (1)$ From equation (1), it follows that

$\frac{1}{λ} = R Z^{2} (\frac{1}{3 ^{2}} - \frac{1}{4 ^{2}}) = R Z^{2} (\frac{1}{9} - \frac{1}{16}) = \frac{7 R Z ^{2}}{9 \times 16} \Rightarrow λ = \frac{144}{7 R}$

Hence, $α = 144$ .

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