How Does an Electron Behave Near a Nucleus?

[ncm2]

I am sure it is easy to do, but I just can't seem to figure the question out. It is 4 parts and I got the first 2 parts. If someone can give me the steps with the numbers (already handed in assignment, and got it incorrect), that would be much appreciated.


1. What is the magnitude of the electric field at a distance of 3.10 ×10-10 m from a neptunium nucleus?
The answer I got is 1.39×1012 N/C.

2. What is the magnitude of the force on an electron at that distance?
2.23×10-7 N F=qE.

3. Treating the electron classically, that is, as a point object that can move around the nucleus at reasonably slow speeds, what is the period of the electron's motion?
The answer is 2.23×10-16 s but I am unable to calculate this.

I tried taking the Force from part 2 and using F=ma. Then using a to find velocity. Then used that to find T.

4. Again treating the electron classically, how fast it it moving?
The answer is 8.72×106 m/s, again no idea what I did wrong but I can't find this answer.



Many thanks.

 

[H_man]

I wouldn't start with F=ma for question 3. I think F = mv²/r would do the trick.

Once you have v you can work out what the distance is for the electron to make one complete orbit (hint, you already have the radius).

And then of course, speed = distance/time.

This gives the answers to both (3) and (4)

 

[baba89]

I would like to provide some guidance on how to approach these questions.

Firstly, it is important to understand the concept of electric field and force. The electric field is a measure of the strength of the electric force at a particular point in space. The force on an object with charge q in an electric field E is given by the equation F=qE.

For the first part of the question, you correctly calculated the electric field at a distance of 3.10 ×10-10 m from the neptunium nucleus. To calculate the force on an electron at that distance, we simply use the equation F=qE, where q is the charge of the electron (-1.6 x 10^-19 C) and E is the electric field you calculated in part 1. This gives us a force of 2.23×10-7 N.

Moving on to part 3, we are asked to find the period of the electron's motion using classical mechanics. This means we can use the equation T=2π√(m/k), where T is the period, m is the mass of the electron (9.11 x 10^-31 kg), and k is the force constant. In this case, the force constant is the electric force between the electron and the nucleus, which we calculated in part 2. So, plugging in the values, we get T=2π√(9.11x10^-31 kg/2.23x10^-7 N) which gives us a period of 2.23×10-16 s.

For the last part, we are asked to find the speed of the electron using classical mechanics. This can be done using the equation v=√(k/m), where v is the speed, k is the force constant, and m is the mass of the electron. Again, we use the force constant we calculated in part 2 and the mass of the electron to get v=√(2.23x10^-7 N/9.11x10^-31 kg) which gives us a speed of 8.72×106 m/s.

In conclusion, it is important to understand the concepts and equations involved in order to solve these types of problems. I hope this helps you understand the steps and calculations involved in finding the period and speed of an electron near a nucleus.