## Textbook 1B.25

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Tiao Tan 3C
Posts: 67
Joined: Wed Sep 30, 2020 9:59 pm

### Textbook 1B.25

"What is the minimum uncertainty in the speed of an electron confined within a lead atom of diameter 350. pm? Model the atom as a one-dimensional box with a length equal to the diameter of the actual atom."

The solution manual assumed that "the uncertainty in the position of the electron is equal to the diameter of the box".
Where did this assumption come from?

Can someone please explain the electron in the box further?
Thanks

Sophia Hu 1A
Posts: 91
Joined: Wed Sep 30, 2020 10:09 pm
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### Re: Textbook 1B.25

Since the problem states that the electron is "confined within a lead atom" I think you would assume that the electron can be found anywhere within the atom, therefore the uncertainty in the position would be 350pm. I also think this would related to the electron in a box.

The electron in a box is another quantum mechanism description of an electron. The box itself is the atom. Therefore, this means that the length of the box is the diameter of the atom. If the electron is bound to the atom it stays in the box as a result of be attracted to the nucleus. To remove an electron, it leaves the box. I think the idea is that the electron can move freely throughout the box so this creates an uncertainty in the position of the electron (which is therefore why the uncertainty in the position of the electron in the problem is the diameter of the box). I think it might also related to how energy levels are quantized, but I'm not exactly sure of this relation. He didn't explain it too much during lecture so I hope this helps.