A hydrogen atom consists of a single proton and a single...

A hydrogen atom consists of a single proton and a single electron. In its ground state the electron is most likely to be found at a distance of 0.529 nm from the proton. Question 2 Retaken 1 / 1 point (a) What is the magnitude of the electric force between the electron and proton. Answer: 8.24x10^-10 N Question 3 Retaken 0.25 / 1 point (b) In a simple model of the atom, known as the Bohr model, the electron orbits the proton in a circle of radius 0.529 nm. How fast is it moving? Hint: The electric force provides the necessary centripetal force. Answer: 2.19x10^6 m/s

Transcript

00:01 Here we're going to use some simple electrical ideas to figure out the energy as needed to ionize the hydrogen atom.

00:12 So these ideas are incorporated in what's called the bore model of hydrogen.

00:20 And much of that model is using classical dynamics and energy ideas.

00:27 So total energy of the electron is just its kinetic plus its potential energy.

00:37 And its potential energy is the electrical value for point charges.

00:45 And we know that both the electron and the proton, we know the charge on both of those.

00:52 The electron's negative e.

00:54 The proton is positive e.

00:56 And their separation were taken as a given as 0 .0529 nanometers.

01:05 So if we put all those numbers in, we calculate what appears to be a small energy, a negative energy, of course, as the two particles attract each other.

01:25 Now, to get the kinetic energy, we are going to need to use newton's second law in order to use f -equals m -a to determine the velocity of the electron.

01:43 So the force on the particle is the electrical or coulomb force.

01:52 I'll write that down.

01:56 And we are just finding the magnitude of the force.

01:59 It is going to change direction, always being directed towards the center of the orbit.

02:07 So we are going to set that force equal to the mass of the electron times its centripetal acceleration.

02:18 But the force we can calculate is k e squared over a squared.

02:30 And that turns out to be what appears to be a small force.

02:43 And now we are going to set that equal to mass times the centripetal acceleration.

02:52 And this is where numbers start to get a little bit crazy.

02:57 Mass of the electron is given in the data over to the left.

03:04 But we get a huge acceleration.

03:08 Any macroscopic object would be in bad shape with this acceleration...