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
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
Get Answers For Free
Most questions answered within 1 hours.