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# In a hydrogen atom, what is the principal quantum number of the electron orbit with a radius closest to 1.0$\mu \mathrm{m} ?$

## 137

Atomic Physics

Nuclear Physics

### Discussion

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##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Jared E.

University of Winnipeg

### Video Transcript

In this exercise, we have to find what is the principal quantum number and of an electorate that's orbiting Ah, hydrogen nucleus with a radius equals to one micro meter. So what we need to do so remember that the radius of the orbit of the end enter your level in a hydrogen atom is given by and square. Sorry and square times. The more radius A zero where a zero is five points. 29 times 10 to the minus 11 meters. Okay, uh, so and square is equal to the radius, divided by a zero. In our case, the radius is ah, one micrometer. So that's tend to them on a six meters, divided by five points. 29 time. Stand to the miners. 11 meters. Okay, so this is 1.89 time. Stand to the fourth, and we can take the square root and find that N is equal to 137. Okay, so this is the principal quantum number of the election in ah, in ah orbit in an orbit that has a radius equal to one micrometer.

#### Topics

Atomic Physics

Nuclear Physics

##### Christina K.

Rutgers, The State University of New Jersey

##### Andy C.

University of Michigan - Ann Arbor

##### Jared E.

University of Winnipeg