Question

A

238

U nucleus is moving in the x

-

direction at 5.0 x 10

5

m/s when it decays into an alpha particle (

4

He) and a

234

Th

nucleus. The alpha

particle moves at 1.4 x 10

7

m/s at 30

°

above the x

-

axis. Find the velocity of the thorium.

[Note:

238

U means a uranium nucleus with a mass of 238 u, where u

is an atomic mass unit. The thorium nucleus

has a mass of 234 u, and the alpha particle’

s mass is 4 u. It is possible to do the problem witho

Answer 1

M = 238 u , m1 = 4 u , m2 = 234 u

v = 5*10^5 m/s , u1 = 1.4*10^7 m/s

from conservation of momentum alonh x direction

Mvx = (m1u1x) +m2v2x

(238*5*10^5) = (4*1.4*10^7*cos(30))+(234*u2x)

u2x = 3.013*10^5 m/s

from conservaiton of momentum along y direction

Mvy = (m1u1y +m2u2y)

0 = (4*1.4*10^7*sin(30) +(234*u2y)

u2y = - 1.2*10^5 m/s

u2 = ((3.013*10^5)^2 +(1.2*10^5)^2)^0.5

u2 = 3.24*10^5 m/s

tan(theta) = -1.2/3.013

theta = 21.7

direction 21.7 degrees below the x axis