have fin Problem The r is called the classical radius of the electron, because t
ID: 2075457 • Letter: H
Question
have fin Problem The r is called the classical radius of the electron, because the electron actually has finite size, but because a free inter acting with photons scatters them as if it had a lower of re. if photons have much In particular, the acquire Probl swal energies than the rest of the electron, the scattering Emc section of free 8Tr Idealize the The completely hydrogen which equ M ionized near a quasar to be from the cen is optically thin to the radiation emerging free electron source luminosity L. Show that each and of intercepts per unit time the energy (8Tre scatters energy all directions. Assume that only the interception process leads to a net transfer of mo ntum, and show that, since the momentum carried by photon is 1/c times its energy, the time-rate of transfer a Ll3cr of momentum per free electron is given by 2re This outward push of the electrons by the radiation pres- sure acts also indirectly on the protons the nuclei of the ionized hydrogen atoms), because strong electrostatic forces tend to make the electron gas and proton gas moveExplanation / Answer
mH=me+mp= mass of hydrogen atom=1.67*10^-24gm=1.67*10^-27kg
L=10^47erg/sec
re=10^-36m , c=3*10^8m/s, G=6.67*10^-11m^3/kg.s^2
then we get M>=2/3*re^2*L/GmHc=2/3* 10^-36^2*10^47/6.67*10^-11*1.67*10^-27*3*10^8
or M>=.019*10^5kg
now lets take a standard stellar mass M=2.02* sun mass=2.02*1.9*10^30kg=3.8*10^30kg
LE=3/2 *MmH*c/re^2=3/2*3.8*10^30*1.67*10^-27*3*10^8/10^-36^2=28.56*10^83 erg/sec
our nearest stellar mass sun has luminosity of 3.8*10^26joules/sec or 3.8*10^33erg/sec
from maximum X-ray luminosity we can say that this stellar mass is moving like accretion disk
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