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.

1 answer

(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.