Question

A ground state hydrogen atom absorbs a photon of light having a wavelength of 92.57 nm. It then gives off a photon having a wavelength of 954.3 nm. What is the final state of the hydrogen atom? Values for physical constants can be found here.

Answer 1

Step 1:

wavelength = 92.57 nm

= 9.257*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 m-1

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

1/9.257*10^-8 = - 1.097*10^7*(1/nf^2 - 1/1^2)

(1/nf^2 - 1/1^2) = -0.9847

1/nf^2 = 1.526*10^-2

nf^2 = 66

nf = 8

Step 2:

wavelength = 954.3 nm

= 9.543*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 m-1

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

1/9.543*10^-7 = 1.097*10^7*(1/nf^2 - 1/8^2)

(1/nf^2 - 1/8^2) = 9.552*10^-2

1/nf^2 = 0.1111

nf^2 = 9

nf = 3

Answer: 3