Final answer:
The wavelength of light associated with the transition from n = 3 to n = 1 in the hydrogen atom is 9.74 × 10^6 meters.
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 formula for the wavelength of the line in the spectrum of hydrogen:
λ = R * (1/n1^2 - 1/n2^2)
where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels, respectively.
In this case, n1 = 3 and n2 = 1. Plugging these values into the formula, we can calculate the wavelength.
Using the Rydberg constant R = 1.097 × 10^7 m⁻¹, the calculation becomes:
λ = 1.097 × 10^7 m⁻¹ * (1/1^2 - 1/3^2)
Simplifying the equation, we get:
λ = 1.097 × 10^7 m⁻¹ * (1 - 1/9)
λ = 1.097 × 10^7 m⁻¹ * (8/9)
λ = 9.74 × 10^6 m⁻¹
Therefore, the wavelength of light associated with the transition from n = 3 to n = 1 in the hydrogen atom is 9.74 × 10^6 meters.