You are here:

# Physics/Physics-calculate the acceleration of the electron from the info given.

Question
Hi, I'm really stuck on this question that I have to do for an assignment.. I've tried to google a formula but I can't find any that seem to fit.. here is the question:

"In the Bohr Model of the hydrogen atom an electron of mass 9.1X10^-31kg is considered to e moving in a circular orbit of Radius 5.3X10^3km s^-1 around a central proton. Calculate the acceleration of the electron."

Thank you very much, Aoife!

For an electron moving in a circular path around the nucleus you will need to use Newton's 2nd Law: SF=m*a
For this orbiting electron the only relevant force will be the electrostatic force and the acceleration is centripetal. Therefore:
SF=Fe=k*q^2/R=m*ac  where k=9*10^9N*m^2/C^2, R is the Bohr Radius R=5.3*10^(-11)m, q is the elementary charge q=1.6*10^(-19)C and m is the mass of the electron m=9.11*10^(-31)kg.
Solving for the centripetal acceleration this becomes:
ac=k*q^2/(m*R)=9.0*10^9*(1.6*10^(-19))^2/(9.11*10^(-31)*5.3*10^(-11))=9.0*10^22m/s^2

Physics