A neutron collides elastically with a helium nucleus (at rest initially) whose mass is four times that of the neutron. The helium nucleus is observed to move off at an angle θ′2=45∘. The neutron's initial speed is 4.2×105 m/s .
Determine the speeds of the two particles, v′n and v′He, after the collision. Express your answers using two significant figures. Enter your answers numerically separated by a comma.
Given,
m2 = 4 m1; theta'2 = 45 deg ; vi = 4.2 x 10^5 m/s
momentum is conserved in all the direction. So along x
mv = 4 m v'He cos45 + m v'n cos(theta)
v = 2 sqrt (2) v'He + v'n cos(theta)
along y
0 = 4m v'He sin45 - m v'n sin(theta)
v'n sin(theta) = 2 sqrt(2) v'He
v'v^2 sin^2(theta) = 8 v'He
from conservation of energy
1/2 m v^2 = 1/2 4m + v'He^2 + 1/2 m v'n^2
v^2 = 4 v'He^2 + v'n^2
putting v'v^2 sin^2(theta) = 8 v'He
v = v'n sqrt (1/2 sin^2(theta) + 1)
putting in first eqn
v = v' n(sin(theta) + cos(theta))
v'n sqrt (1/2 sin^2(theta) + 1) = n'n sin(theta) + cos(theta)
sin(theta)/cos(theta) = 4
theta = 76 deg
4.5 x 10^5 = v'n (sin76 + cos76)
v'n = 3.71 x 10^5 m/s
v'n sin(theta) = 2 sqrt(2) v'He
3.71 x 10^5 sin76 = 2 x 1.414 v'He
v'He = 1.27 x 10^5 m/s
A neutron collides elastically with a helium nucleus (at rest initially) whose mass is four times...
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