Determine the energy of the electromagnetic radiation

[F.B]

Please i really need help I am sorry to have had to make a second thread but i really need to finish this.


2. The electron and positron each have a rest mass of 9.11 x 10^-31 kg. In a certain experiment, an electron and positron collide and vanish, leaving only electromagnetic radiation after the interaction. Each particle is moving at a speed of 0.20c relative to the laboratory before the collision. Determine the energy of the electromagnetic radiation.

First of all do i have to solve this question like a collision problem, if i do there is no after situation.

Anyways i think i have to solve for Ek.

So Et=Ek + Erest

Et=mc^2/sqrt(1-v^2/c^2)
Et=9.11 x 10^-31 x (3.00 x 10^8)^2/sqrt(0.96)
Et=8.37 x 10^-14
Erest = 8.2 x 10^-14
Ek= 8.37 x 10^-14 - 8.2 x 10^-14
Ek= 1.7 x 10^-15

But this answer isn't right. The books has 0.615 Mev

2. The Big Bang, which is a theory predicting the origin of the universe, is estimated to have released 1.00 x 10^68 J of energy. How many stars could half this energy create, assuming the average star's mass is 4.00 x 10^30 kg.

I did this but again my answer is different from the back of the book.

E=mc^2
m=1.00 x 10^68/(3.00 x 10^8)^2
=1.11 x 10^51

=1.11 x 10^51/4.00 x 10^30
=2.78 x 10^20 kg

The book's answer is 1.39 x 10^20 stars. What did i do wrong.

3. A supernova explosion of a star with a rest mass of 1.97 x 10^31 kg, produces 1.02 x 10^44 J of kinetic energy and radiation.
a) How many kilograms of mass are converted to energy in the explosion?

This one i have no idea how to do.

Please i really need help with all these questions i really have to get these done soon.

 

[Astronuc]

1. The rest mass of the electron/positron is 0.511 MeV, and that is the minimum photon energy when annihilation occurs. Just at the relativistic kinetic energy from each electron to each photon. Think total energy.

2. How many stars could half this energy create, . . . ?

3. Again assume total energy. Some of supernova's rest mass is converted to radiation and kinetic energy of the material.

What is the mass equivalent of 1.02 x 10^44 J of kinetic energy and radiation?

 

[quicknote]

I would suggest approaching these questions by using the equation E=mc^2, where E is energy, m is mass, and c is the speed of light. This equation relates the energy of an object to its mass and the speed of light.

1. For the first question, you are correct in using the equation Et=Ek+Erest. However, the values you used for the rest mass (9.11 x 10^-31 kg) and the speed (0.20c) are for the individual particles, not for both of them combined. The total mass of the system before the collision would be 2(9.11 x 10^-31 kg) = 1.82 x 10^-30 kg. Also, the velocity used in the equation should be the relative velocity between the particles, which in this case would be 0.40c (since they are moving in opposite directions). So the correct calculation would be:

Et= 1.82 x 10^-30 kg x (3.00 x 10^8 m/s)^2/sqrt(1-0.40^2)
Et= 8.19 x 10^-14 J
Erest= 9.11 x 10^-31 kg x (3.00 x 10^8 m/s)^2/sqrt(1-0.40^2)
Erest= 8.19 x 10^-14 J
Ek= 0 J

Since the particles have equal and opposite momenta, they cancel each other out and there is no kinetic energy. The total energy of the electromagnetic radiation would be 8.19 x 10^-14 J.

2. For the second question, you are correct in using the equation E=mc^2. However, you should use the total energy released by the Big Bang (1.00 x 10^68 J) and divide it by the average mass of a star (4.00 x 10^30 kg). This will give you the total number of stars that could be created from the energy released by the Big Bang. So the correct calculation would be:

N= 1.00 x 10^68 J / (4.00 x 10^30 kg x (3.00 x 10^8 m/s)^2)
N= 1.39 x 10^20 stars

3. For the third question,