how can this conservation of energy of alpha decay question be explained conceptually

https://postimg.cc/FYfq97zP

the ans to this is D but I am confused by the working given by physmathstutor, as when writing the equation:

MαVα^2 + MthVth^2 = 2E,

im confused on how they got Mth = (234Mα/4V).

otherwise I assumed the ans was A, but Im not completely sure why its D. Is there another way to get this answer via explanation?

(edited 6 months ago)

Reply 1

Joinedup

well the first thing I'd think about is conservation of momentum. the alpha is going to have a much greater velocity than the Th nucleus

and KE=1/2mv^2
so large difference in v is going to dominate large difference in mass and the alpha is going to make off with a lot more than half the total energy, but less than all the energy.

4/238 - is less than 1/2
4/234 - is less than 1/2
1/2 - is equal to 1/2
234/238 - is more than 1/2 but less than 1
1 - is equal to 1

There's only one option that's even in the right area