Calculating Electron Revolutions per Second in Electric Force Field

[guru]

An electron of mass (m=9.1*10^(-31)kg) orbits a proton at a distance of 5.3*10^(-11)m. The proton pulls on the electron with an electric force of 9.2*10^(-8)N.
How many revolutions per second does the electron make?

This is what I did:

m=9.1*10^(-31)kg
v=5.3*10^(-11)m
T=9.2*10^(-8)N

V=sqrt(rT/m)= 23147876.27 m/s

angular velocity (w) = (v/r) = 4.38^(16) rad/s
w*(1 rev/(2(pi)rad)) = 9.17*10^9 rev/s

I was told the answer was wrong.
Please help

 

[kenhcm]

The electrostatic force serves as the centripetal force. It is given by F = mrw^2. Once w has been determined, w/(2 pi) will be the frequency.


Kenneth

 

[wais]

!

Your calculations are correct, but your final answer is in revolutions per second instead of electron revolutions per second. To convert to electron revolutions per second, we need to take into account the fact that the electron is orbiting the proton, which has a much larger mass. This means that the electron's velocity is not solely determined by the electric force, but also by the proton's gravitational force. We can use the equation for centripetal force to calculate the electron's velocity in terms of electron revolutions per second:

F = mv^2/r

Solving for v:

v = sqrt(Fr/m)

Plugging in the values given:

v = sqrt((9.2*10^-8 N)(5.3*10^-11 m)/(9.1*10^-31 kg)) = 23147876.27 m/s

Now, to convert to electron revolutions per second, we need to divide by the circumference of the electron's orbit (2*pi*r):

v/(2*pi*r) = (23147876.27 m/s)/(2*pi*(5.3*10^-11 m)) = 2.18*10^16 electron rev/s

So, the electron makes 2.18*10^16 revolutions per second in this electric force field.