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For a hydrogen atom, calculate the wavelength of light (in m) that would be emitted for the orbital transition of n(initial) = 3 to n(final) = 1. Submit an answer to four significant figures. The Rydberg constant is 1.09678 x 10⁷ m⁻¹.

Answer :

The wavelength of the light emitted for the orbital transition from n = 3 to n = 1 is 0.975m.

For hydrogen, the wavelength of the light emitted for the orbital transition of n = 3 to n = 1 is given by,

1/λ = R(1/n²-1/n'²)

Where,

R is the Rydberg's constant,

n is the initial orbital,

n' is the final orbital,

Putting values,

1/λ = 1.097(1/1-1/9)

1/λ= 1.097 x 8/9

λ = 0.975 m.

Hence, the wavelength of the light emitted is 0.975m.

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