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# The wavelengths of the Paschen series for hydrogen are given by\$$\frac{1}{\lambda}=R_{\mathrm{H}}\left(\frac{1}{3^{2}}-\frac{1}{n^{2}}\right) \qquad n=4,5,6, \ldots$$(a) Calculate the wavelengths of the first three lines in this series. (b) Identify the region of the electromagnetic spectrum in which these lines appear.

## a) $1875 \mathrm{nm}, 1281 \mathrm{nm}, 1094 \mathrm{nm}$b) $\mathrm{IR}$

Atomic Physics

Nuclear Physics

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##### Andy C.

University of Michigan - Ann Arbor

LB
##### Jared E.

University of Winnipeg

### Video Transcript

in this exercise have to calculate the wavelengths of the 1st 3 lines of the passion Siris of the hydrogen atom. The passion Siri's happens when, and an Adam that's originally at the stage and transitions to the third state and emits ah, folding in the transitioning and the wavelength. Lunda of the emitted photon obeys the equation. One over. Lambda equals there with Burke Constant time. 1/3 square 1/3 square, minus one over in square. Okay, so Lunda is equal to one over our age times one over a nine, minus one over and squared. Where are age there would bear Constant is 1.97 times 10 to the seventh meters to the minus. What the first line happens when n equals four transitions to the third level. So the wave ling of this transition is one over 1.97 times 10 to the seven meters the minus one times will nine. Mine is 1 16 and this is equal to 1.8 75 times since of them minus seventh meters, which is sorry 10 to the minus six meters, which is 1875 millimeters. Okay, The second transition happens from the fifth to the third, and we have to do a very similar calculation. But instead of 1/16 we have won 25th and this is equally true travel. 100 and 82 centimeters. Third line is from the sixth energy level to the third. So again, there were very constant. 1/9. Mine is one 36. So what we have is 1000 and 94 millimeters. Okay, this is the the answer to question a and in question. But you have to say, Ah, in what region of the electromagnetic spectrum these these three way wings are in. Okay, notice that the infrared region off the electromagnetic spectrum is a starts at about 700 centimeters and goes until about one millimeter, and these three wavelength all fall within this range. So for that reason, you can say that they are infrared ready

#### Topics

Atomic Physics

Nuclear Physics

##### Andy C.

University of Michigan - Ann Arbor

LB
##### Jared E.

University of Winnipeg