Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each of the following transitions.

Question

Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each of the following transitions. (Express your answer in inverse seconds to three significant figures.)

n=7→n=3

n=5→n=1

n=9→n=5

Answer 1

We'll first calculate the wavelength λ, and then the frequency

1 / λ = R (1/n_f² - 1/n_i²)

R = 1.097x10⁷ m^-1

n_f = 3

n_i = 7

1 / λ = (1.097x10⁷ m^-1) (1/9 - 1/49) = (1.097x10⁷ m^-1) (0.0907)

1 / λ = 994979 m^-1

λ = 1.01x10^-6 m

Converting this to frequency (v), we have ...

c = λv

v = c/λ = 3x10⁸ m/s / 1.01x10^-6 m

v = 2.97x10¹⁴ s^-1 (answer in inverse seconds to 3 sig. figs.)

You can do the others in the same manner.