Calculating Energy and Wavelength help?

Question

Calculate the energy in joules and the wavelength in nanometers of the spectral line produced in the hydrogen spectrum when an electron falls from the third Bohr orbit to the first. (Report your answer using three significant figures.) In which region of the electromagnetic spectrum (UV, visible, or infrared) is the line?

Answer 1

∆E = R_H (1/n_f² - 1/n_i²)

∆E = change in energy = ?

R_H = -2.179x10^-18 J

n_f = final energy level = 1

n_i = initial energy level = 3

∆E = -2.179x10^-18 J (1/1 - 1/9) = -2.179x10^-18 J (0.8889)

∆E = -1.05x10^-18 J (negative since energy is released when falling from higher to lower energy level)

To find the wavelength, use E = hc / λ

E = energy = 1.05x10^-18 J

h = Planck's constant = 6.626x10^-34 Js

c = speed of light = 3x10⁸ m/s

λ = wavelength = ?

Solving for λ, we have ...

λ = hc / E = (6.626x10^-34 Js)(3x10⁸ m/s) / 1.05x10^-18 J

λ = 1.89x10^-7 m = 189 nm