Assume an electron is in a circular orbit about a proton, held in place by the e

Question

Assume an electron is in a circular orbit about a proton, held in place by the electric field of the proton at an orbital radius of r = 1.0 Angstroms. (Note: This is an order-of magnitude problem … it's the power of 10 that matters).

a) [5 pts] Using the balance between the centripetal (centrifugal force), what is the orbit speed V of the electron, assuming it is in a classical, “planetary orbit” with a radius of 1.0 Angstroms?

b) [5 pts] What is acceleration of experienced by this electron in circular motion?

c) [5 pts] Use the Larmour formula, P = e2 a2 / c3 , to calculate the amount of radiated power.

d) [10 pts] Over what time interval does the radiation carry away as much energy as the orbit kinetic energy, 0.5 meV2 of the electron in its original orbit? For this estimate, ignore the orbit decay resulting from the radiation of electromagnetic waves.

e) [5 pts] What does this imply about the life-time of atoms in a hypothetical world in which only the laws of classical mechanics apply?

Explanation / Answer

Solving first 4 parts

(a)Balancing force

Ke*e/r^2=mv^2/r

we got v=1.6*10^4 m/s

(b) a=v^2/r=2.53*10^(18) m/s^2

(c) using your formula of power

P=e^2*a^2/c^3=6.06*10^(-27) W

(d) time=KE/P=19192.6 sec

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