What is the final state of the hydrogen atom?

Question

A ground state hydrogen atom absorbs a photon of light having a wavelength of 92.27nm. It then gives off a photon having a wavelength of 384.3nm What is the final state of the hydrogen atom? Where h is Planck's constant (6.626x10^ -34), c is the speed of light (2.998x10^ 8 m/s), and the wavelength in meters. 

Answer 1

Use Rydberg Equation

1/wavelength=R(1/initial^2 - 1/final^2)

Initial and final are the initial and final energy levels where an electronic transitions to.

R is the Rydberg constant

R=1.096775×10^7

For the 92.97 absorption, initial=1, solve for final

1/92.92×10^-9=R(1/1^2 - 1/final^2)

(1/92.97×10^-9)*(1/1.096775×10^7)=1/1^2 - 1/final^2

final=8

When 384.3 wavelength is released

n=8 will be initial level. Solve for final level.

-1/383.4×10^-9=R(1/8^2 - 1/final^2)

(-1/383.4×10^-9)*(1/1.096775×10^7)=1/8^2 - 1/final^2

final=2

When n=2 the electron will land at that level.