CBSE Class 12 · 2017 · Modern PhysicsShort Answer

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Calculate the shortest wavelength of light emitted in the Paschen series of the hydrogen spectrum. Which part of the electromagnetic spectrum does it belong to? (Given: Rydberg constant

R = 1.1 \times 1 0^{7} m^{- 1}

Answer: $λ \approx 818 nm$ ; infrared.

Solution

For the Paschen series

n_{f} = 3

; the shortest wavelength (series limit) corresponds to

n_{i} = \infty

\frac{1}{λ} = R (\frac{1}{3 ^{2}} - \frac{1}{\infty ^{2}}) = \frac{R}{9} = \frac{1.1 \times 1 0 ^{7}}{9} = 1.22 \times 1 0^{6} m^{- 1} .

λ = 8.18 \times 1 0^{- 7} m = 818 nm .

This lies in the infrared region.

λ \approx 818 nm (infrared)

CBSE Class 12 Board · 2017 · Subjective

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