Question

A hydrogen atom in the ground state absorbs a photon of wavelength 95.0 nm.
What energy level does the electron reach?

This excited atom then emits a photon of wavelength 434.1 nm.
What energy level does the electron fall to?

-I know this question has already been asked on Chegg but each question I go to has different calculations and I can't get the right answer.

Answer 1

1)

wavelength = 95 nm

= 9.5*10^-8 m

Here photon will be captured and it will excite the atom

1/lambda = -R* (1/nf^2 - 1/ni^2)

R is Rydberg constant. R = 1.097*10^7

1/lambda = -R* (1/nf^2 - 1/ni^2)

1/9.5*10^-8 = - 1.097*10^7*(1/nf^2 - 1/1^2)

(1/nf^2 - 1/1^2) = -0.9596

1/nf^2 = 4.045*10^-2

nf^2 = 25

nf = 5

Answer: 5

2)

wavelength = 434.1 nm

= 4.341*10^-7 m

Here photon will be emitted

1/lambda = R* (1/nf^2 - 1/ni^2)

R is Rydberg constant. R = 1.097*10^7

1/lambda = R* (1/nf^2 - 1/ni^2)

1/4.341*10^-7 = 1.097*10^7*(1/nf^2 - 1/5^2)

(1/nf^2 - 1/5^2) = 0.21

1/nf^2 = 0.25

nf^2 = 4

nf = 2

Answer: 2