# Rotation period of electron orbiting a proton

• SorenaJ
In summary, the conversation discusses an electron rotating around a proton in a circular orbit and how to calculate the rotation period. The equations used are F=(k*q^2)/r^2 and arad=(angular velocity)^2*r. The force is found to be 2.3*10^-8 N and the angular velocity is 15.2 rad/s, resulting in a rotation period of 0.41 seconds. However, there is a discrepancy in the calculation and it is suggested to always use units to avoid errors. It is also mentioned that the radial acceleration is caused by the electric force, but is mitigated by the electron's mass.
SorenaJ

## Homework Statement

An electron is rotating around a proton (at rest) in a perfect circular orbit. If the radius of the orbit is r=10^-10 m, how long is the rotation period [hint: the radial acceleration is entirely due to the electric force]

k=9*10^9
q=1.6*10^-19

1. F=(k*q^2)/r^2

## The Attempt at a Solution

I found the force by equaiton 1., and I got 2.3*10^-8 N ((9*10^9)(1.6*10^-19)^2))/((10^-10)^2)
I tried equation 2. to get (angular velocity)=sqrt(F/r) and got 15.2 rad/s
This means that it is 2.4 rev/s (by dividing by 2pi) and 0.41 seconds per orbital period.
That is like the world's slowest electron. Where did I go wrong?

Is Force equal to acceleration? ... or is there something missing?
always use units, to avoid slip-ups like this.

Maybe not. It just says that the radial acceleration is entirely due to the electric force. To find the radial acceleration do I just need to say a=F/m?

well, the radial acceleration is caused entirely by the electric force, but it is mitigated via (spread thru-out) the electron mass
= .911×10-30 kg .

## 1. What is the rotation period of an electron orbiting a proton?

The rotation period of an electron orbiting a proton is approximately 1.6 x 10^-23 seconds.

## 2. How is the rotation period of an electron orbiting a proton calculated?

The rotation period is calculated using the equation T = 2πr/v, where T is the period, r is the radius of the orbit, and v is the velocity of the electron.

## 3. Why is the rotation period of an electron orbiting a proton important?

The rotation period is important because it determines the frequency at which the electron orbits the proton, which in turn affects the energy levels and behavior of the atom.

## 4. Does the rotation period of an electron orbiting a proton change?

No, the rotation period of an electron orbiting a proton remains constant as long as the atom remains in the same energy state. However, it may change when the atom absorbs or releases energy.

## 5. How does the rotation period of an electron orbiting a proton differ in different elements?

The rotation period of an electron orbiting a proton can vary slightly between different elements, as it is affected by the atomic mass and number of protons in the nucleus. However, the differences are typically very small and have little impact on the overall behavior of the atom.

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