Question

A hydrogen atom in the ground state absorbs energy and makes a transition to the n = 3 state. The atom returns to the ground state by emitting two photons. What are the wavelengths of the two photons?

(A) 6.56 x 10-7m, 1.22 x 10-7m
(B) 6.56 x 10-7m, 5.45 x 10-7m
(C) 3.43 x 10-7m, 1.22 x 10-7m
(D) 5.45 x 10-7m, 3.43 x 10-7m

Answer 1

at n= 3 λ = 656 nm

at n= 2 λ = 121.58 nm

Step-by-step explanation:

Given details

transition of hydrogen atom from n = 2 to n = 3 state

Difference in energy between n = 3 state and n = 2 state :

`= 2.18*10^(-18) * [1/4 - 1/9] J = 3.03 * 10^(-19) J`

so, energy of photon is given as
`=(h*c)/(\lambda)`

`E = 3.03*10^(-19)</p><p>` So solve for wavelength

so, λ
`= (6.626*10^(-34)*3*10^8)/(3.03*10^(-19))m`

=
`6.56*10^(-7) m`

= 656 nm

for second transition,

energy transmitted is given asΔE
`=(h* c)/(\lambda)`

and it is calculated as
`= 2.18*10^(-18)*[1/1 -1/4] J`

E = 1.635*10-18 J solving for wavelength in ENERGY equation we get

so,
`\lambda' = 1.2158*10^(-7)` m

= 121.58 nm