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Calculate the wavelength of light associated with the transition from n = 3 to n = 1 in the hydrogen atom.

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Final answer:

The wavelength of light associated with the transition from n = 3 to n = 1 in the hydrogen atom is approximately 656 nm, corresponding to the red part of the visible spectrum.

Step-by-step explanation:

To calculate the wavelength of light associated with the transition from n = 3 to n = 1 in the hydrogen atom, we can use the Rydberg formula:

1/λ = RH[(1/nf2) - (1/ni2)]

Where λ is the wavelength, RH is the Rydberg constant for hydrogen (approximately 1.097373 x 107 m-1), nf is the final energy level (n=1 in this case), and ni is the initial energy level (n=3 in this case).

Plugging in the values, we get:

1/λ = (1.097373 x 107 m-1)[(1/12) - (1/32)]

Solving for λ, we find:

λ ≈ 656 nm

Therefore, the wavelength of light associated with the transition from n = 3 to n = 1 in the hydrogen atom is approximately 656 nm, which corresponds to the red part of the visible spectrum.

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