Calculate the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom undergoes the transition from the energy level 𝑛=7 to the level 𝑛=1

Answer 1

Just to add to the answer provided by @Eric M:

The Rydberg formula can be viewed as 1/λ = R(1/n_f² - 1/n_i²)

λ = wavelength in meters

R = Rydberg constant = 1.0973x10⁷ m^-1

n_f = final level = 1

n_i = initial level = 7

1/λ = 1.0973x10⁷ m^-1 (1/1² - 1/7²)

1/λ = 1.0973x10⁷ m^-1 (1 - 0.0204) = 1.0973x10⁷ m^-1 (0.9796)

1/λ = 1.075x10⁷ m^-1

λ = 9.30x10^-8 m

λ = 93.0 nm

Answer 2

This is an application of the Rydberg formula, which can be found here: https://en.wikipedia.org/wiki/Rydberg_formula#For_hydrogen

Plugging n_1 = 1 and n_2 = 7 (just so the sign is positive) gives you a wavelength of 93.03 nanometers.