Entery level Mass-energy equivalence questions

[letsfailsafe]

Homework Statement

The diagram shows a proton moving with Ek of (0.178)(10^-12)J towards a stationary nucleus X. The proton hits X and is absorbed.

The resulting nucleus splits into two alpha particles, which move off in the directions shown with equal Ek of (1.481)(10^-12)J

1. Calculate the mass equivalence of the net energy release during the collision.
2. Calculate the rest mass of the nucleus X. The mass of a proton is (1.673)(10^-27) kg and the mass of an alpha particle is (6.645)(10^-27)kg

Homework Equations

E=mc²

The Attempt at a Solution

First question I have no idea how to do that.

second question, I simply added the proton mass + alpha particle mass (which is a wrong answer since energy is used for binding energy)

I sort of get the concepts but can't do them mathematically...
Please help me step by step.
Answers:
1. 3.09X10^-29
2. 11.6X10^-27

 

[apelling]

The guiding principle is mass/energy conservation.

initial (rest mass energy + kinetic energy)= final (rest mass energy + kinetic energy)

Question 1 is just concerned with the increase of kinetic energy expressed as a mass equivalence.
Question 2 just use the above equation. Be careful to include all rest masses and kinetic energies and express them all in the same unit.

 

[letsfailsafe]

Sorry, I really do not know how to do these questions...

 

[apelling]

For question 1 find the difference between the initial kinetic energy and the final kinetic energy. Then use E=mc^2 to convert energy to a mass equivalent.

 

[letsfailsafe]

Thank you I've finally got and understood the first question.
I still don't know how to solve the second question... :/

 

[apelling]

The increase in kinetic energy must have come from a reduction in rest mass. In other words the mass of the two alphas is less than the mass of X and the proton. You have values for the rest mass of the alphas and the proton and the mass equivalent of the kinetic energy gained.