Chapter 30, Problem 25Q

To determine

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.