Question

A 238U nucleus is moving in the x-direction at 4.3×10⁵ m/s when it decays into an alpha particle (4He) and a 234Th nucleus. The alpha moves at 1.9×10⁷ m/s at 24 ∘ above the x-axis.

Part A

Find the speed of the thorium nucleus.

Part B

Find the direction of the motion of the thorium nucleus.

Answer 1

Here ,

initial speed , u = 4.3 *10^5 m/s

for the alpha particle ,

v1 = 1.9 *10^7 * (cos(24) i + j * sin(24))

let the velocity of thorium is v2

Using conseration of momentum

238 *u = 234 * v2 + 4 * v1

238 * 4.3 *10^5 i = 4 * 1.9 *10^7 * (cos(24) i + j * sin(24)) + 234 * v2

v2 = 1.406 *10^5 i - 1.32 *10^5 j m/s

v2 = sqrt(1.406^2 + 1.32^2) * 10^5 at arctan(-1.32/1.406) degree

v2 = 1.93 *10^5 m/s at -43.19 degree

the speed of thorium is 1.93 *10^5 m/s

b)

the direction of the motion is -43.19 degree from the positive x -direction