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Hydrogen spectrum

Find the largest and shortest wavelengths in the Lymen series

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Hard

Solving time: 4 mins

Find the largest and shortest wavelengths in the Lymen series for hydrogen. In what region of the electromagnetic spectrum does each series lie?

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Book:

Master Resource Book in JEE Main Physics (Arihant)

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Find the largest and shortest wavelengths in the Lymen series for hydrogen. In what region of the electromagnetic spectrum does each series lie?

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Text solutionVerified

The transition equation for Lymen series is given by,

\frac{1}{λ} = R (\frac{1}{1 ^{2}} - \frac{1}{n ^{2}}), n = 2, 3, \dots

The largest wavelength is corresponding to

n = 2

∴ \frac{1}{λ _{m a x}} ∴ λ_{m a x} = 97 \times 1 0^{7} (\frac{1}{1} - \frac{1}{4}) = 0.823 \times 1 0^{7} m = 1.2154 \times 1 0^{- 7} m = 1215 A n g s t ro m

The shortest wavelength corresponds to

n = \infty

∴ \frac{1}{λ _{m i n}} = 1.097 \times 1 0^{7} (\frac{1}{1} - \frac{1}{\infty})

or

λ_{m i n} = 0.911 \times 1 0^{- 7} m

= 911 A n g s t ro m

Both of these wavelengths lie in ultraviolet (UV) region of electromagnetic spectrum.

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Question Text	Find the largest and shortest wavelengths in the Lymen series for hydrogen. In what region of the electromagnetic spectrum does each series lie?
Topic	Atoms
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	129