Classical model of a hydrogen atom. Assume an electron is in a circular orbit ab
ID: 1655837 • Letter: C
Question
Classical model of a hydrogen atom. 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. a) 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) What is acceleration of experienced by this electron in circular motion? c) Use the Larmour formula, P = e^2 a^2/c^3, to calculate the amount of radiated power. d) Over what time interval does the radiation carry away as much energy as the orbit kinetic energy, 0.5 meV^2 of the electron in its original orbit? For this estimate, ignore the orbit decay resulting from the radiation of electromagnetic waves. e) 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
a)
me = mass of electron = 9.1 x 10-31 kg
qe = qp = 1.6 x 10-19
centripetal force = electric force of attaraction between electron and proton
me v2 /r = k qe qp /r2
( 9.1 x 10-31)v2 /(1 x 10-10) = (9 x 109) (1.6 x 10-19)2 /(1 x 10-10)2
v =1.6 x 106 m/s
b)
acceleration is given as
a = v2/r = (1.6 x 106)2/(1 x 10-10) = 2.56 x 1022 m/s2