- #1
afeser
I have a sample problem :
Photon, with energy E, is absorbed by m. Then, mass m becomes m' (i think it's relativistic mass). Calculate the new mass.
My teacher solved the problem as follows;
Please help me! What am I missing?
Thanks a lot...
Photon, with energy E, is absorbed by m. Then, mass m becomes m' (i think it's relativistic mass). Calculate the new mass.
My teacher solved the problem as follows;
P1=( E/c, P3dphoton); // momentum of the photon
P2=(mc, 0); // momentum of the stationary mass
Length=((P1+P2)|(P1+P2)); // which is to be conserved
But my solution is a bit different because I think we should only sum up the 3 dimensional values, and the relativistic mass will be γ*m where γ is 1/(1-(v/c)2)1/2P2=(mc, 0); // momentum of the stationary mass
Length=((P1+P2)|(P1+P2)); // which is to be conserved
=(P1|P1)+2*(P1|P2)+(P2|P2)
=0+2*E*m+m2c2; // (P1|P1) is 0
=m'2*c'2; // since it is invariant
Therefore:
m'=m*(1+2E/mc2)1/2
=0+2*E*m+m2c2; // (P1|P1) is 0
=m'2*c'2; // since it is invariant
Therefore:
m'=m*(1+2E/mc2)1/2
Pinitial=(m*c, 0, 0, 0)
Pfinal=(γ*m*c, P3dphoton)
and (Pinitial|Pinitial)=(Pfinal|Pfinal) because it's invariant
Also, since (Pphoton|Pphoton)=0,
we have (P3dphoton|P3dphoton)=(E/c)2,
which implies γ=(1+E2/(m*c2)2)
then we have m'=m*γ=m*(1+E2/(m*c2)2)1/2 which is obviously different from the first solution.
Which solution is correct? I think the first, of course, because we conserve the 4th dimensional vector, however claiming (m'c)2 is invariant makes me uncomfortable because that means Pfinal=(γ*m'*c, Px, Py, Pz), where γ*m'*c factor should be E/c (as I learned from Wikipedia), but it's not.(m'=γ*m -> γ*m'*c=γ2*m'*c, which is not E/c=γ*m*c) Pfinal=(γ*m*c, P3dphoton)
and (Pinitial|Pinitial)=(Pfinal|Pfinal) because it's invariant
Also, since (Pphoton|Pphoton)=0,
we have (P3dphoton|P3dphoton)=(E/c)2,
which implies γ=(1+E2/(m*c2)2)
then we have m'=m*γ=m*(1+E2/(m*c2)2)1/2 which is obviously different from the first solution.
Please help me! What am I missing?
Thanks a lot...