In this problem you will estimate the lifetime of electromagnetic energy at a ra

Question

In this problem you will estimate the lifetime of electromagnetic energy at a rate given by P = -2kq^2a^2/3c^3, where a is acceleration. Assuminmg that the electron is one Bohr radius (0.0529 nm) from the center of the hydrogen atom. Calculate the energy of the electron and determine how long it wil take for all of this energy to be converted into electromagnetic waves, assuming that the rate calculated in part b remains constant through the electron's motion. b. was -2.90 eV/s. this is c, which is 4.69 x 10^11s

There is always one every chapter, this was it for this chapter! Thanks!

Explanation / Answer

The kinetic energy of the electron is

K = (1/2)mv^2

where m is mass of electron(9.1 * 10^-31 kg) and v is speed of electron

v = (2pi * r/T)

where r = 0.0529 nm = 0.0529 * 10^-9 m and T = 4.69 * 10^11 s

let t be the time taken for all of this energy to be converted into electromagnetic waves

we know that

v = u + at

where u = 0 and a is acceleration of electron

or t = (v/a)

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