Question

A. Determine the wavelength of the light absorbed when an electron in a hydrogen atom makes a transition from an orbital in which n=2 to an orbital in which n=7. Express the wavelength in nanometers to three significant figures.

B. An electron in the n=6 level of the hydrogen atom relaxes to a lower energy level, emitting light of λ=93.8nm. Find the principal level to which the electron relaxed. Express your answer as an integer.

Can you explain it in details? Where each number comes from

Answer 1

A)

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/lambda = - 1.097*10^7* (1/7^2 - 1/2^2)

lambda = 4.00*10^-7 m

lambda = 400 nm

Answer: 400. nm

B)

wavelength = 93.8 nm

wavelength = 9.38*10^-8 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)

1/9.38*10^-8 = 1.097*10^7*(1/nf^2 - 1/6^2)

(1/nf^2 - 1/6^2) = 0.9718

1/nf^2 = 0.9996

nf^2 = 1

nf = 1

Answer: 1