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Problem 18 Medium Difficulty

A hydrogen atom initially in its ground state $(n=1)$ absorbs a photon and ends up in the state for which $n=3$. (a) What is the energy of the absorbed photon? (b) If the atom eventually returns to the ground state, what photon energies could the atom emit?

Answer

a) 12.1 $\mathrm{eV}$
b) $12.1 \mathrm{eV}, 1.89 \mathrm{eV}, 10.2 \mathrm{eV}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Farnaz M.

Other Schools

Jared E.

University of Winnipeg

Video Transcript

in this exercise, we have a hydrogen atom that's initially in the ground state. So and why is the initial state equals one and jumps to the third state after absorbing a photo? So unethical street in question? A we want to calculate bought is the energy of the observed Fulton. So due to conservation of energy, you the energy of the fulton A gamma is just the final energy off the hydrogen atom, which is e three. The energy of the third level. Mine is the initial energy you want. Now, remember that the energy of the 10th level of the hydrogen atom is minus 13.6 electoral votes divided by in square. And for that reason de Goma is 13.6 times 1/1 squared, which is this one minus 1/3 square, which is nine. Let me just write nine a little better here. So this is equal to 12.1 electron volts. That's the energy of the absorbed Fulton. Okay, in question be I'll have the electric coming back to the ground state, So it, uh, it's initially initially in the third state, and it transitions back to the final state n f equals one, and we want to calculate all the possible energies all the possible, the energies of the fulton that the the atom can emit when doing this transition. So there are three possible transitions for the Adam to go from the third energy level to the 1st 1 you can go directly from the third to the first. In that case, the energy of the Fulton is just the energy of the third energy level. Mine is the energy of the 1st 1 So that's 13.6 one minus 19 which is 12.1 of the crime votes. It can go from the third energy level to the second and then go to the second from the second to the first and the energy of a photon. In that case, in the first transition from the third energy level to the 2nd 1 is three minutes to, and that's 13.6 eloquent votes times one fourth man is 19 Okay, so this is 1.89 electoral votes and the energy of the Fulton when ah, the Adam transitions from the second energy level to the 1st 1 is a two man is the one. So this is 13.6 one minus 1/4 and it is 10.2 electoral votes. Okay, so these are the energies of the Fulton's that the atom can emit when transition transitioning from the third energy level to the 1st 1

Universidade de Sao Paulo
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Farnaz M.

Other Schools

Jared E.

University of Winnipeg