Special relativity and lost mass

[Fisicks]

Homework Statement

When a uranium nucleus at rest breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process?

Homework Equations

K=Ymc^2 - mc^2
Im sure you can figure out what i mean by Y lol.

The Attempt at a Solution

I am stumped because although we do know the KE, we don't know the velocity of the fragments which would give us the rest energy of the fragments. Any help?

Thanks for your time,
Fisicks

 

[Fisicks]

bump!

 

[turin]

Homework Statement

When a uranium nucleus at rest breaks apart in the process known as fission in a nuclear reactor, the resulting fragments have a total kinetic energy of about 200 MeV. How much mass was lost in the process?

At first glance, the information given in the problem seems to be insufficient. You need to know which isotope of uranium that you started with and what are the resulting decay fragments. However, with access to some basic data (say, over the internet), you can fill in the gaps. Since fission initiated by neutron absorption adds to the ambiguity of the question, you should guess from the context of the question which isotope you are dealing with, and then, with the assumption of spontaneous fission, should should be able to determine the decay products.

 

[Fisicks]

hmm. Wikipedia makes me believe to use Uranium 235. Is this sentence accurate?

"For uranium-235 (total mean fission energy 202.5 MeV), typically ~169 MeV appears as the kinetic energy of the daughter nuclei, which fly apart at about 3% of the speed of light"

Using this i could either plug .03 in for v and solve for the final mass or i can do 200-169=mc^2 to get the final mass as well. Right?

 

[rwisz]

I understand your confusion. In order to calculate the lost mass in this scenario, we need to use the equation E=mc^2, where E is the total energy (kinetic + rest) and m is the mass. We also need to take into account the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

In this case, the total energy before and after the fission process must be equal. We know the total kinetic energy after the process (200 MeV), and we also know that the total rest energy of the uranium nucleus before the process is equal to its mass (m) times the speed of light squared (c^2). Therefore, we can set up the following equation:

200 MeV + m(c^2) = m'c^2

Where m' is the mass of the fragments after the fission process. We can rearrange this equation to solve for m':

m' = m - (200 MeV/c^2)

Therefore, the lost mass in this process is equal to 200 MeV divided by c^2, which is approximately 2.2x10^-29 kg. This may seem like a small amount, but in the world of nuclear reactions, even small changes in mass can lead to large amounts of energy.

I hope this helps to clarify the concept of lost mass in special relativity. Remember, when dealing with nuclear reactions, it is important to take into account both the kinetic and rest energies to fully understand the system. Keep up the good work in your studies of physics!