Principal Quantum Number: Chemistry

Question

An electron in an excited state of hydrogen undergoes a transition to the n = 5 level. In the process, a photon of energy 6.03×10^-20 J is emitted.



What was the value of the principal quantum number for the higher energy level?

Answer 1

Use the relations:

 

1/λ = R(1/5² - 1/n²)

 

E  = hc/λ = hcR(1/5² - 1/n²)

 

R = 1.097 x 10⁷ m^-1  [the Rydberg constant]

 

E = hcR(1/5² - 1/n²)

 

You have E, and you know the values of h, c, and R.  Plug the numbers into the last equation above and solve for n.  You know that n > 5. Do the math and finish from here.