Find the wavelength of the spectral line corresponding to the transition in hydrogen from n = 6 state to n = 3 states. (Ans: 1094 nm)



Data Given:


Excited state = n = 8

Lower state = p = 1


∴ Rydberg constant = R = 1.097 ｘ 10⁷ m⁻¹


To Find:

The wavelength of the spectral line = λ =  ?



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Solution:

Using the Rydberg formula for electron transition from excited state p to lover state n

1λ = R( 1p²-1n²)

by putting values

1λ = 1.097 ｘ 10⁷ m⁻¹ ( 13²-16²)

1λ = 1.097 ｘ 10⁷ m⁻¹ ( 19-136)

1λ = 1.097 ｘ 10⁷ m⁻¹ 4-136

1λ = 1.097 ｘ 10⁷ m⁻¹ 336

1λ = 1.097ｘ10⁷m⁻¹12


by flipping the fraction on both sides of the equation we get


λ =  121.097ｘ10⁷m⁻¹


or


λ = 10.938 ｘ 10⁻⁷ m


or


λ = 1093.8ｘ 10⁻⁹ m


λ = 1094 nm ------------Ans.



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