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# The wavelengths of the Lyman series for hydrogen are given by$$\frac{1}{\lambda}=R_{\mathrm{H}}\left(1-\frac{1}{n^{2}}\right) \qquad n=2,3,4, \ldots$$(a) Calculate the wavelengths of the first three lines in thisseries. (b) Identify the region of the electromagnetic spectrum in which these lines appear.

## a) $121.5 \mathrm{nm}, 102.5 \mathrm{nm}, 97.20 \mathrm{nm}$b) far ultraviolet

Atomic Physics

Nuclear Physics

### Discussion

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##### Andy C.

University of Michigan - Ann Arbor

##### Aspen F.

University of Sheffield

##### Jared E.

University of Winnipeg

### Video Transcript

in this exercise, we have to calculated three first wave wings off the lineman Siri's and we have a one over. Lambda is equal to the Rittenberg constant times one miners one over in square and the 1st 3 wavelengths are gonna happen. A transition and equals two to the first level enables three to the first level and any goes four to the first level. And we can calculate Lunda. Yes, one over there would bear constant times. One miners, one over and square. Okay. And there would bear constant, as always, is one point 097 times 10 to the seventh meters, the minus one. So have the transition. The wavelength, due to the transition from the second to the first, is equal to 1/1 0.97 times 10 to the seventh Leaders to the minus one times 1/2 square. So it's mine is 1/4. This is equal to 1.215 times 10 to the minus seventh meters. This is the same as 1 to 1.5, 121.5 centimeters. The transition from the third to the first level. So This is 1.97 times 10 to the seventh meters. The man is 11 miners 1/9 and this is equal to 102.5 centimeters from the force. The Firth to the first. This is again 1.97 Time sent them to the seventh. Leaders to the man is one one. Mine is 1 16 and this is equal to 97. Coined two centimeters. Okay, this is the answer to question A in question, be we have Teoh say what? In what region of the electromagnetic spectrum these wavelengths lie Notice that the ultraviolet, uh, part of the spectrum It starts at 10 centimeters and go and goes until about 400 centimeters. Okay, so all these three way blanks 97 102 and 121. They lie between 10 and a meters and 400 meters. So for that reason, they are old dra violent

#### Topics

Atomic Physics

Nuclear Physics

##### Andy C.

University of Michigan - Ann Arbor

##### Aspen F.

University of Sheffield

##### Jared E.

University of Winnipeg