Problem

Verify that the ground state energy $E_{0}$ is 13…

02:32

Problem 9 Medium Difficulty

Look up the values of the quantities in $a_{B}=\frac{h^{2}}{4 \pi^{2} m_{e} k q_{e}^{2}}$ and verify that the Bohr radius $a_{B}$ is $0.529 \times 10^{-10} m$

Answer

$0.52984 \times 10^{-10} \mathrm{m}$

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Physics 103

College Physics for AP® Courses

Chapter 30

Atomic Physics

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Christina K.

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Video Transcript

so force Iranian sees h squared for I squared e Okay, Q e squared and lose. Just, uh, put, um, while use off in each parameter here. So H is planks constant, which is seeks point, uh, 6 to 6, 10 to the minus 30. Force power. And this is squared and derided on for I squared. So pi is around One for two squared and we have m e, which is eloquence. Merce One. Uh, so no. 9.10 nine 10 to the minus 31 and incomes kun's constant. Okay, which is They're owned eight Fine 99 Tend toward the names and last term here he's just continue here. He's, uh q e Electron's charge, which is one point seeks you too. Tell him. I guess 19 s o. He can check these values by yourself. So again they seize H plan is constant. This is pie. This is a lactose mass. This is cool, is constant and this is in the interest charge and then a B becomes so I will square some terrible's here. So we have punks constant squared and this number becomes for nine. 10 my 10 to the minus 67 and the same for And then pi squared, which becomes nine. So in Come and the incomes Ellicott's mus, which is which isn't ah, square. So it's the same. And think how schools constant also unchanged and then we hope accused square Q E squared, which becomes 2.56 weeks 10 minus 38. So what we, uh, did here is we just squared these 22 numbers to terms the sworn Cure square and then this 18 square. Everything else is the same old. So also, we squared by so and within first in such kind of calculations when we have 10 uh, powers and just numbers, we need to separately, uh, calculate numbers and 10 spoke 10 powers. So we have 10 hours, I will just circle them, and everything else is just numbers. So, what is the total tens power here? And you? You carefully look, uh, the total Hilton Power tensed our worries. 10 minus, uh, 10 1 over 10. Tow the seven to 1/7 hour. So when he sees 10 97 And what are these? Numbers aren't It's numbers, huh? Zero point five two. Lying 10 minus three. Because look at all the numbers are in the denominator, so we don't have tens power here. But while older numbers are in the denominator, the number we would we will couple e becomes where we stroll. Uh, and we have 10 to the minus three additional powers. So in total, A D would be five to Maddie. 10 miners take meters.

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