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The electrostatic force causes the electron to move around the circle at a constant speed. In this type of problem, the centripetal force must be equal to the electrostatic force.

Fc = m * v^2 ÷ r

Fe = k * q1 * q2 ÷ r^2

m * v^2 ÷ r = k * q1 * q2 ÷ r^2

v = √[(k * q1 * q2) ÷ (r * m)

k = 9 * 10^9

The charge of an electron and proton is 1.60 * 10^-19 Coulomb. m is the mass of the electron. This is 9.11 * 10^-31 kg.

k * q1 * q2 = 9 * 10^9 * 1.60 * 10^-19 * 1.60 * 10^-19 = 2.304 *10^-28

r * m = 5.41 * 10^-11 * 9.11 * 10^-31 = 4.92851 * 10^-41

v = √(2.304 *10^-28 ÷ 4.92851 * 10^-41)

The speed of the electron is approximately 2.16 * 10^6 m/s. The numbers that I used to solve this problem came from two tables in my physics book. I hope this is helpful for you.

In this model the centripetal force mv^2/r is provided by the electrostatic attraction k*q1*q2/r^2

Set them equal.

Plug in the known values of r, m (mass of electron), q1 and q2 (charges of proton and electron) and k (Coulomb constant). Solve for v.