Moseis T. answered 03/18/20
Science and Math Tutor
This is a momentum conservation question funnily enough.
Since the atom was at rest before the decay we know in the original momentum is 0, and will be 0 after the decay as well.
So if the net momentum must be zero, then we know the momentum of the daughter nucleus and the helium nucleus must be the same.
we can use the equation T = P2 /(2m), since we are doing alpha decay m = 4u for the helium nucleus.
So: 4.7 Mev = P2/(8u) so P = 6.1318 with the appropriate units.
This is the same momentum the daughter nucleus has after to conserve momentum
using the equation again we have KE = 6.13182/224 = 0.167 Mev
hope this helps!