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.