How stable is an atom? Recall from your mechanics class, that to keep a body, su

Question

How stable is an atom? Recall from your mechanics class, that to keep a body, such as a Low Earth Orbit (LEO) satellite, in orbit, it needs to be given a certain initial (tangential) velocity. Essentially this velocity will cause a centripetal force that counteracts the gravitation pull of the earth. Earth For a hydrogen atom, the average distance between the nucleus and the electron is about 5x10 m. From Coulomb's law, calculate the speed at which the electron has to move to stay in a stable orbit around the nucleus. How does that speed compare to the speed of light? Hint: To get a stable orbit, the centripetal force pushing out should match the Coulomb force pushing in The centripetal force is equal to Fcentripeta,--

Explanation / Answer

Coulomb,sforce must be equal to the centripetal force to get the constant speed in the orbit

Coulomb's force = centripetal force

k*q1*q2/r^2 = m*v^2/r

q1 = q2 = 1.6*10^-19 C

k = 9*10^9 N.m^2/C^2

m is the mass of the electron = 9.11*10^-31 kg

v is the speed of the electron

then v = sqrt(k*q1^2/(m*r)) = sqrt(9*10^9*1.6*1.6*10^-38/(9.11*10^-31*5*10^-11)) = sqrt(5.05*10^12)

v = 2.25*10^6 m/s is the required speed of the electron in the orbit

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