Orbital Frequency of Electron-Positron Pair: Calculating 1.0nm Separation

[soccerref14]

Can someone tell me how or an idea on how to start this problem?

A positron is an elementary particle identical to an electron except that its charge is +e. An electron and a positron can rotate about their center of mass as if they were a dumbbell connected by a massless rod. What is the orbital frequency for an electron and a positron 1.0nm apart?

 

[praharmitra]

Find out the center of mass of the entire system. You can then assume that two particles are orbiting around their mutual center of mass. The velocity can be calculated from their mutual attractive force.

 

[baba89]

To calculate the orbital frequency of an electron-positron pair at a separation of 1.0nm, we can use the formula for Kepler's third law:

T^2 = (4π^2 / GM) * r^3

Where T is the orbital period, G is the gravitational constant, M is the combined mass of the electron and positron, and r is the separation distance.

To find the orbital frequency, we can simply take the inverse of the orbital period, which gives us:

f = 1/T = 1 / √[(4π^2 / GM) * r^3]

Substituting in the given values for the mass of an electron and positron (9.109 x 10^-31 kg) and the separation distance (1.0nm = 1 x 10^-9 m), we can solve for the orbital frequency.

f = 1 / √[(4π^2 / (9.109 x 10^-31 kg) * (1 x 10^-9 m)^3]

f = 1 / √[1.145 x 10^-44]

f = 8.8 x 10^22 Hz

This means that the electron and positron will complete one full orbit around their center of mass 8.8 x 10^22 times per second.

As for an idea on how to start this problem, you can begin by identifying the relevant variables and equations, and then plugging in the given values to solve for the desired quantity. It may also be helpful to visualize the problem and draw a diagram to better understand the setup of the electron-positron pair orbiting each other.