Final answer:
The frequency of light when transitioning from n=4 to n=1 is -290.24 Hz.
Step-by-step explanation:
The frequency of light during the transition from n=4 to n=1 can be calculated using the formula:
f = c / λ
where f is the frequency, c is the speed of light (approximately 3 x 10^8 m/s), and λ is the wavelength.
The wavelength can be calculated using the formula:
λ = R (1/n₁² - 1/nf²)
where R is the Rydberg constant (approximately 1.097 x 10^7 m⁻¹), n₁ is the initial level (n=4 in this case), and nf is the final level (n=1 in this case).
Plugging in the values:
λ = 1.097 x 10^7 (1/4² - 1/1²) = 1.097 x 10^7 (1/16 - 1/1) = 1.097 x 10^7 (1/16 - 1) = 1.097 x 10^7 (1/16 - 16/16) = 1.097 x 10^7 (-15/16) = -1.033 x 10^6 m⁻¹
Using the value of λ, we can calculate the frequency:
f = c / λ = 3 x 10^8 / (-1.033 x 10^6) = -290.24 Hz
Since frequency cannot be negative, the magnitude of the frequency is 290.24 Hz.