An electron in a hydrogen atom relaxes to the n = 4 level, emitting light of 114 THz. What is the value of n for the level in which the electron originated?

Answer 1

Frequency (f) = 114 THz x 1 Hz / 10^-12 THz = 114x10¹² Hz = 114x10¹² s^-1

Let's find the wavelength (λ)

c = λf

λ = c / f = 3x10⁸ m/s / 114x10¹² s^-1

λ = 2.63x10^-6 m

Next we can use 1 / λ = R (1/n_f² - 1/n_i²) where R = 1.097x10⁷ m^-1 and n_f = final level and n_i = initial level

1 / 2.63x10^-6 m = 1.097x10⁷ m^-1 (1/16 - 1/x²)

0.03466 = 0.0625 - 1/x²

1/x² = 0.0278

x = 6

Thus, it appears that the electron originated in level n = 6 and fell to level n = 4.