A ground state hydrogen atom absorbs a photon of light having a wavelength of 94.9 nm. What is the final state of the hydrogen atom?

Question

A ground state hydrogen atom absorbs a photon of light having a wavelength of  What is the final state of the hydrogen atom?

Answer 1

E = hc/λ

E = energy of photon

h = Plank's constant = 6.626x10^-34 Jsec

c = speed of light = 3x10⁸ m/sec

λ = wavelength = 94.9 nm = 94.9x10^-9 m

E = 6.626x10^-34 Jsec x 3x10⁸ msec^-1 / 94.9x10^-9 m

E = 2.09x10^-18 J = energy of photon with a wavelength of 94.4 nm

Now use ∆E = 2.179x10^-18 J (1/(1)² - (1/n²)

2.09x10^-18 J = 2.179x10^-18 J - 2.179x10-18 J / n²

n² = 24.5

n = ~5

So, it looks like the final state of the hydrogen atom would be n = 5.