An electron in the n = 6 level emits a photon with a wavelength of 410.2 nm. To what energy level does the electron move?

Answer 1

E = hc/λ = (6.626x10^-34 Js)(3x10⁸ m/s) / 410.2x10^-9 m)

E = 4.85x10^-19 J

∆E = -R_H (1/n_f² - 1/n_i²)

∆E = 4.85x10^-19 J

R_H = -2.179x10^-18 J

nf = final level = ?

ni = initial level = 6

4.85x10^-19 J = (-2.179x10^-18 J)(1/x² - 1/36)

4.85x10^-19 = -2.179x10^-18 / x² + 6.06x10^-20

x ≈ 2

Check the math as I did a bit of rounding and came up with n_i = 2