Question

I am confused on how to even start this problem...

A ground state H atom absorbs a photon of wavelength 94.91 nm, and its electron attains a higher energy level. The atom then emits two photons: one of wavelength 1281 nm to reach an intermediate level, and a second to reach the ground state.
a) What higher level (n=?) did the electron reach?
b) What intermediate level (n=?) did the electron reach?
c) What was the wavelength of the second photon emitted?

Thanks

Answer 1

For #a.
delta E1 = hc/wavelength but change 94.91 nm to meters first. Then use
delta E1 = 2.180 x 10^-18*[(1/n₁²)-(1/n₂²)] where n<sub>1 = 1 (the first shell of hydrogen; i.e., the ground state). Solve for N₂. I obtained 5 for n2. (That isn't n^2; that is n^2 = 25 + change but round to 25.).

part b.
Go through the same procedure for the 1281 nm line and determine n1. N1 is the final state and n=5 (that's n from part A). Solve for n1. I obtained 3 for that.
That leaves part c to do. The difference in energy must be the amount from n=1 to n=5 minus the energy from n=5 to n=3. The easiest way to do that is to use the above formula and plub in n1 = 1 and n2 = 3.
Show your work if you get stuck.