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Question 42

The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly __ nm.

Smallest Lyman wavelength = 91 nm → $$R = 1/(91 \times 10^{-9})$$.

Largest Balmer: $$3 \to 2$$: $$\frac{1}{\lambda_B} = R(1/4-1/9) = 5R/36$$. $$\lambda_B = 36/(5R) = 36 \times 91/5 = 655.2$$ nm.

Largest Paschen: $$4 \to 3$$: $$\frac{1}{\lambda_P} = R(1/9-1/16) = 7R/144$$. $$\lambda_P = 144/(7R) = 144 \times 91/7 = 1872$$ nm.

Difference = $$1872 - 655.2 = 1216.8 \approx 1217$$ nm.

The answer is Option 4: 1217 nm.

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