finding recoil speed?

Question

A uranium nucleus (mass 238 u), initially at rest, undergoes radioactive decay. After an alpha particle (mass 4.0 u) is emitted, the remaining nucleus is thorium (mass 234 u). If the alpha particle is moving at 0.0350 times the speed of light, what is the recoil speed of the thorium nucleus? (Note: "u" is a unit of mass; it is not necessary to convert it to kg.)

Answer 1

use conservation of momentum (where momentum p=mv):
p initial = 0 (v=0)
p final = p(alpha) + p(thorium) = 0
4.0*0.0350*c +234*V = 0
you will probably get a negative number indicating that it is moving in the opposite direction of the alpha particle.

hope it helps=)

Answer 2

Just use the law of conservation of momentum.

The momentum of the alpha particle must be equal and opposite to the momentum of the thorium nucleus.

momentum = mass x velocity.

You will end up with a ratio of masses, so the units don't matter.

Answer 3

The mass of the α particle is actually 4u/√(1-.035²) so the Velocity of the nucleus, Vn is
Vn = 4*.035/(234*.998) ≈ .006 c

Of course, you might want to correct the mass of the nucleus for relativistic effects too...........! The result will still be noticably different than 4*.035/234.