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Monochromatic radiation of wavelength λ is incident on a hydrogen sample in ground state.Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. Find the value of λ. Rydberg constant =1.09 X 10-7 m-1

Monochromatic radiation of wavelength λ is incident on a hydrogen sample in ground state.Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. Find the value of λ. Rydberg constant =1.09 X 10-7 m-1

Grade:12

2 Answers

Vikas TU
14149 Points
7 years ago
from the eqn. for ground state
n(n-1)/2 = 6
n^2 – n – 12 = 0
n^2 – 4n + 3n – 12 = 0
(n-4) (n+3) = 0
n = 4
Therfore,
1/λ = R*1^2(1/1^2 – 1/4^2)
1/λ = R*(1 – 1/16) => 15R/16
λ = 16/15R   = 16*10^7/(15 *1.09) is the answer.    = 0.978593 * 10^7 meter.
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

from the eqn. for ground state
n(n-1)/2 = 6
n^2 – n – 12 = 0
n^2 – 4n + 3n – 12 = 0
(n-4) (n+3) = 0
n = 4
Therfore,
1/λ = R*1^2(1/1^2 – 1/4^2)
1/λ = R*(1 – 1/16)
=> 15R/16
λ = 16/15R
= 16*10^7/(15 *1.09) is the answer.
= 0.978593 * 10^7 meter

Thanks and Regards

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