Quantum Numbers and Ground vs Excited State

Question

If an excited H atom EMITS a 95nm photon when relaxing to the ground state, what was the principle quantum number of the excited state? 

 

a. 1

b. 2

c. 3

d. 4

e. 5

Answer 1

Use the Rydberg formula.

 

1/λ = R(1/n₁² - 1/n₂²)

 

n₁ = 1  (ground state)

n₂ = n = ?  (excited state)

R = Rydberg constant = 1.097373156850865 x 10⁷ m^-1

λ = 95 x 10^-9 m

 

1/λ = R(1/1² - 1/n²) = R(1 - 1/n²)

 

Solve for n and get

 

n = √[λR/(λR - 1)]

 

Plug in the numbers.  You might have to round the answer to the closest integer.