An excited hydrogen atom emits light with a frequency of 1.141x10^14 Hz to reach the energy level of which n=5
(a)in what principle quantum did the electron begin.
(b) using the calculated wavelength, predict the spectral series and the region on the electromagnetic spectrum.
(a) To calculate the initial principle quantum number (n) of the electron, we can use the formula for the frequency of emitted light by a hydrogen atom:
f = R*(1/n_final^2 - 1/n_initial^2)
where f = 1.141x10^14 Hz, n_final = 5, and R is the Rydberg constant (3.29x10^15 Hz).
Plugging in these values and solving for n_initial:
1.141x10^14 = 3.29x10^15*(1/5^2 - 1/n_initial^2)
n_initial^2 = 25/(25 - 3.29) = 25/21.71
n_initial = √(25/21.71) ≈ 1.22
Therefore, the electron began in the n=1 principle quantum level.
(b) Next, we can calculate the wavelength of the emitted light using the frequency:
c = f*λ
where c is the speed of light (3.00x10^8 m/s) and λ is the wavelength.
Plugging in the values:
λ = c/f = 3.00x10^8/1.141x10^14 ≈ 2.63x10^-6 m.
The spectral series corresponding to this wavelength is the Paschen series, which falls in the infrared region of the electromagnetic spectrum.