Electron Motion Near Nucleus: Calculating Period and Velocity

In summary, the magnitude of the electric field at a distance of 5.00 ×10−10 m from a radon nucleus is 4.95×1011 N/C. The magnitude of the force on an electron at that distance is 7.94×10-8 N. Using classical calculations, the period of the electron's motion can be found using the equation T=2Pi/omega, and the speed of the electron can be found using the equation a=v^2/r. However, the attempts to solve for omega and velocity using these equations have been unsuccessful. Additional help is needed.
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Homework Statement


What is the magnitude of the electric field at a distance of 5.00 ×10−10 m from a radon nucleus?
=4.95×1011 N/C
What is the magnitude of the force on an electron at that distance?
=7.94×10-8 N
Now here is where I am getting stuck..
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? &
Again treating the electron classically, how fast it it moving?


Homework Equations


T=2Pi/omega
a=v^2/r
f=mr omega^2


The Attempt at a Solution



i tried solving for omega by plugging in the force, radius and mass of radon. then square rooting the answer. so ill have omega and then i take 2 pi over it right? for the period.. that's not working.
then i tried solving for the velocity by taking the force * radius / mass then square rooting that as well to find the velocity and that is wrong...

i don't know where i am going wrong.. any help would be great.

thanks!
 
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1. What is an electron?

An electron is a subatomic particle with a negative charge that orbits around the nucleus of an atom.

2. What is the role of an electron near the nucleus?

The electron near the nucleus is responsible for holding the atom together. Its negative charge balances out the positive charge of the nucleus, creating a stable atom.

3. What is the distance between an electron and the nucleus?

The distance between an electron and the nucleus is not fixed and can vary depending on the energy level of the electron. However, on average, the distance is on the order of 10^-10 meters.

4. How does an electron's energy change near the nucleus?

As an electron gets closer to the nucleus, its energy decreases. This is because the electron is attracted to the positively charged nucleus and is held in a lower energy state.

5. Can an electron be found inside the nucleus?

No, according to the laws of quantum mechanics, an electron cannot exist inside the nucleus. The probability of finding an electron inside the nucleus is extremely low.

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