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

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To calculate the orbital frequency of an electron and positron 1.0nm apart, one must first determine the center of mass of the system, which is located at the midpoint due to their equal mass. The attractive force between the electron and positron can be derived from Coulomb's law, and this force will allow for the calculation of their velocity. Using the velocity and the radius of their orbit, the orbital frequency can be determined through the relationship between frequency, velocity, and radius. Understanding these principles is essential for solving the problem effectively. The calculations will yield the desired orbital frequency for the electron-positron pair.
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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?
 
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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.
 

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