What is the correct velocity of an electron in a bound orbit around a proton?

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The discussion focuses on calculating the velocity of an electron in a bound orbit around a proton, specifically at a distance of 2 x 10^-8 cm. The user equates the centrifugal force (Fc = v²/r) and the electrostatic force (Fe = e²/r²) to derive the electron's velocity. The initial calculation yields an incorrect velocity of 11.5 x 10^-6 cm/s, prompting requests for clarification. Key errors identified include incorrect unit handling and a miscalculation in the final step.

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LukasMont
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Good evening!

The question states: 9. Electron in bound orbit about proton. Suppose that an electron moves in a circular orbit about a proton at a distance of 2 X l0^-8 cm. Consider the proton to be at rest. (a) Solve for the velocity of the electron by equating the centrifugal and electrostatic forces.

Considering that the elementary charge (charge of the electron is e = 4.8 x 10^-10 statcoloumbs), working on the cgs system, I equated the centrifugal force Fc=v²/r and the eletrostatic force Fe= e²/r². My way of solving the problem was:

Fc=Fe,
v²/r = e²/r²
v²= e²/r
v= (e²/r)¹/²
v= (2.3x10^-19/2x10^-8)¹/²
v = 11.5x10^-6 cm/s.

Which is clearly a way down from the correct value. Could anyone please help me?

Thanks!
 
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LukasMont said:
Fc=v²/r
Is the electron mass 1 g? Always write out the units!
 
Also your last calculation step is wrong. v = (11.5x10-12)1/2 which is not 11.5x10-6. But see also Orodruin's comment.
 

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