Question

Calculate the wavelength, in nm, of the photon that is released from a hydrogen atom when the atom's electron moves from n=8 to n=2. Please show all work.

Answer 1

We know that 1/λ = R [ 1/n1^2 - 1/n2^2] , λ = wavelength

Given that electron in a hydrogen atom undergoes the transition from the energy level n = 8 to the level n = 2

i.e. n1= 2 , n2= 8

Then,

1/λ = R [1/n1^2 - 1/n2^2]

= R [ 1/2^2 - 1/8^2]

= R [ 1/4- 1/64]

= R (15/64)

1/λ = R (15/64)

λ = (64/15) (1/R)

= (64/15) ( 91.17 nm) ( since R = 1.09678 x 10^-2 nm^-1 then 1/R = 91.17 nm)

= 389 nm

wavelength λ = 389 nm

Therefore,

walength of photon released from hydrogen atom = 389 nm