## Physics: Principles with Applications (7th Edition)

i. The momentum before the decay was 0, and the total momentum is conserved. The two products must move in opposite directions with equal and opposite momentum vectors. ii. The thorium nucleus and the $\alpha$ particle have the same momentum. Mv = mV. For the product of mass and velocity to have the same magnitude, the smaller mass alpha particle has the greater velocity. iii. Assume the products are moving slowly enough that classical mechanics equations are valid. The KE is related to the momentum by $KE=\frac{p^{2}}{2m}$. The thorium nucleus and the $\alpha$ particle have the same momentum, so the smaller-mass alpha particle has the greater kinetic energy.