Consider the following energy levels of a hypothetical atom: E4 −1.91 × 10−19 J E3 −6.11 × 10−19 J E2 −1.25 × 10−18 J E1 −1.65 × 10−18 J (a) What is the wavelength of the photon needed to excite an electron from E1 to E4?

Wavelength =  1.362 x 10-7 m

Explanation:

ΔE = hc/λ

λ = hc/ΔE

hc = (6.626 x 10-34 Js)(3 x 108 m/s) = 1.9878 x 10-25 J m

λ = (1.9878 x 10-25) / ΔE, with ΔΕ in J, λ in meters

from E1 to E4

ΔE = E4 - E1 = [(-1.91 × 10-19) - (-1.65 × 10-18)] J = 1.459 x 10-18 J

Inserting the value of ΔΕ into the equationabove, we have;

λ = (1.9878 x 10-25) / (1.459 x 10-18) m = 1.362 x 10-7 m