
Which has greater momentum, velocity and kinetic energy when a 238U nucleus decays into a 234Th nucleus and an alpha particle.

Answer to Problem 25Q
Solution:
a ) 234Th nucleus and an alpha particle have same momentum
b)The particle has greater velocity
c)the alpha particle has more kinetic energy
Explanation of Solution
When a 238U nucleus decays into a 234Th nucleus and an alpha particle.
(a)The momentum before the decay was zero, hence the total momentum after the decay will also be zero. When a 238U nucleus decays into a 234Th nucleus and an alpha particle since there are only two decay products, 234Th nucleus and an alpha particle must move in opposite directions with equalmagnitude of momentum. Thus, (c)is the correct choice: both the same.
(b)Since the products 234The nucleus and the alpha particle have the same momentum, the one with the smallest mass will have the greater velocity. The alpha particle has smaller mass compared to thorium Thusoption (b)is the correct choice: the alpha particle.
(c)the kinetic energy of moving particle is given by KE = p2 /2m. Where p is the momentum and m is the mass. Since the particles have the same momentum, the one with the smallest
mass will have the greater kinetic energy. Thus, (b)is the correct choice: the alpha particle.
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