00:01
Hello guys, i'm here to show this problem.
00:02
So an electron in a circular orbit emits synchrotron radiation and an expression of the energy radiated particle per turn is, which is given in the question.
00:18
So delta e is equal to 4 pi e square, beta square, gamma, divided by 3r.
00:26
So where r is the radius of the orbit? beta is the v upon c and gamma is the one minus beta square and the whole power is minus half so evaluate the energy radiated by the one five and ten gigavoltage electron is one kilometer circular orbit so now it is given indication so four one so we need to find the four for the first part for one electron total energy of the electron is one giga electron and one electron's rest mass energy so we know that the electrons rest mass energy is equals to 0 .511 mega electron and the relativistic mass of electron m is equal to m 0 divided by root of 1 minus b a square so it is the relativistic mass so here m is equals to m not multiplied by uh so the gamma factor gamma factor means gamma is equal to m divide by m so is equals to m c squared divided by m c square if you multiply and divide by the c squared so it is equals to gamma is equal to m not c square multiplied gamma divided by m not c square so it's m so we can say that it is also equal to total energy divided by e rash energy.
02:05
So now the total energy is 1 giga -electron volt which is equals to 10x3 meta -electron and the rest energy is equal to 0 .511 electron mega -elof -ton volt.
02:19
So now we put the values here so gamma is equal to 10x3 divided by 0 .511.
02:26
It is equal to 1956 .95 and the value of beta is equal to beta is denoted by v.
02:34
So now we put all the values here.
02:36
So beta is equal to v.
02:38
And gamma are comma is equal to 1 upon root of 1 minus v .a upon c square and it is also denoted by 1 minus beta square because the value of v upon c is beta and the power is minus 1 by we can put the values here so beta is equals to root of 1 minus 1 upon gamma square which is equal to 0 .99 and we also know that the gamma is equals to 1 km the distance r is equal to 1 kilometer which is 10 a pha 3 so the energy radiated by 1 giga electron volt is equal so the energy radiated by 1 giga electron volt is equal to delta e is equal to 4 5 e square beta square r the power 4 divided by 3 r so it's gamma square gamma squared by 3 r so now we put all the values here so it is equal to delta e is equal multiplied 3 .14 multiplied the value of e which is 0 .992 square the value of beta which is 1956 .95...
