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# An isolated atom of a certain element emits light of wavelength 520. nm when the atom falls from its fifth excited state into its second excited state. The atom emits a photon of wavelength 410. nm when it drops from its sixth excited state into its second excited state. Find the wavelength of the light radiated when the atom makes a transition from its sixth to its fifth excited state.

## 1.94 $\mathrm{\mu m}$

Atomic Physics

Nuclear Physics

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### Video Transcript

In this exercise, we have an Adam that transitions from the fifth excited states to the 2nd 1 and emits a fulton that has a wavelength of 529 meters. Ah, it also transitions from the sixth to the second excited state. And and it's, ah, full now that has a wavering on the prime equals to 410 in a meters. And we want to find what is the wavelength? Love the two prime of the folding limited by the Adam when the Adam transitions from the fifth, except matter of Mr from the sixth excited state to the fifth Excited State. Okay, so what I'm gonna do is I'm gonna write the energy off the fold ins for each Ah, for each situation here. So the energy in the first process the energy of the Fulton Ego Mom, without the prime, for now, you cover is able to age see over London. Lunda is the wavelength. And this is equal to the energy of the fifth excited state, minus the energy of the second excited state. Okay, so I'm gonna like this in the second situation. We have that the energy e Goma prime is equal to e HC or loved a prime. And this is the energy of the sixth excited state minus the interview of the 2nd 1 And in the case we want if we wanna work with, we have the the energy E to prime Gamma is equal to age see over limit of prime and this is equal to the energy Of the sixth, said state, mine is the image of the fifth Excited State. Okay. Ah So what we want to do here is to isolate Linda to prime and to find what e six and e five are. And for that, I'm gonna use the two equation that are highlighted in blue. So first and then isolate the five and the five is equal to H C over London plus two is six is age see over lim the prime plus two. So this means that we can substitute this into the equation that's highlighted in green and we gather age see over London to prime. It's better if I just separate this. It beats. It's see over them the two prime. It's equal to six, which is h see over on the prime, plus into minus five, which is H Cyril under minus apple. Uh, pleasure To which because of the miners in front of the five, there's also a minus here. So the e choose cancel out and we have a C over lumber to prime equals a C over London prime minus H c over London. So the H sees cancel out. And when we have, I'm gonna Right here in the center is one over. Linda to prime is equal to one over Lambda Prime minus one over Lunda eso won over London to prime is equal to London A miner's limb, The prime over Lundell. Um, the prime So long the chip prime is equal to love. The Linda prime over Lum Devine is Linda Prime and we have that How Lunda is 520 centimeters times 410 and two meters. That's 1 to 2 over 520 minus 410 centimeters and this is equal to on the to pry is equal to 1938 centimeters, which is approximately one point 94 micro meters. And this is the answer