The Bohr theory of the hydrogen atom neglects gravitational...

Name: Problem 38, Chapter 27: College Physics
Uploaded: 2021-09-28T18:46:34-08:00
Duration: 2 min 43 s
Channel: Brian Francisco
Description: The Bohr theory of the hydrogen atom neglects gravitational forces between the electron and the proton. Make a calculation to justify this omission. [Hint: Find the ratio of the gravitational and electrostatic forces acting on the electron due to the proton.]

The Bohr theory of the hydrogen atom neglects gravitational forces between the electron and the proton. Make a calculation to justify this omission. [Hint: Find the ratio of the gravitational and electrostatic forces acting on the electron due to the proton.]

Key Concepts

Gravitational Force

Gravitational force is the attractive interaction between two masses, as described by Newton's law of universal gravitation. This force is proportional to the product of the masses and inversely proportional to the square of the distance between their centers. In the context of atomic particles, although gravity is universal, its effect is extremely weak compared to other forces.

Electrostatic Force

Electrostatic force is the interaction between electrically charged particles, governed by Coulomb's law. It is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This force is much stronger than gravitational force when dealing with charged subatomic particles like electrons and protons.

Force Ratio Calculation

The force ratio calculation compares the magnitude of gravitational force to that of the electrostatic force. By dividing the gravitational force by the electrostatic force, one can quantify how negligible gravity is relative to electromagnetic interactions at the atomic scale, justifying its omission in models like that of the hydrogen atom.

Bohr Model

The Bohr model of the hydrogen atom is an early quantum model that describes electrons in fixed orbits around the nucleus with quantized angular momentum. The model simplifies the atomic system by considering only the dominant electromagnetic interactions and neglecting gravitational forces, which are insignificant on this scale.

Transcript

00:01 So if we want to compare two forces, the easiest thing is to take the ratio of the two.

00:06 And we know for gravitational force, we have this gravitational constant times the product of the two masses, divided by the square of the distance between them.

00:19 And there's a little bit of a typo there, which would be r squared, not r sub two.

00:26 And similarly, for the electrostatic forces, we have our kulams constant.

00:30 Then we have the product of the two charges.

00:33 And then we have squared distance between them.

00:39 10 of the minus 19 kouloms.

00:42 So when we take the ratios, the distance between them or the bore radius actually gets canceled out, right? because you're going to have 1 over r squared divided by 1 over r squared and that goes away.

00:52 You're going to get the ratio of the two constants and then the ratio of the two products.

00:58 Just taking a look at a couple numbers here, you can sort of qualitatively figure this out.

01:03 I mean, you'll work it out and you can get an answer.

01:05 Well, first off, let's do that.

01:06 If you just plug everything in, 6 .67, 10 to the minus 11 for g, about 9 times 10 to the 9 for k, 9, 10 to the minus 31 for the electron mass, so on, you'll get something like 4 times 10 to the minus 40.

01:24 So that's comparing the gravitational force to the electrostatic force...

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