An unstable atomic nucleus of mass 17.0 × 10–27 kg which is at rest disintegrates into three particles. One of?
An unstable atomic nucleus of mass 17.0 × 10–27 kg which is at rest disintegrates into three particles. One of the particles, of mass 5.00 × 10–27 kg, moves in the y direction with speed 4.20 Mm/s. Another, with mass 8.40 × 10–27 kg, moves in the x direction with speed 5.30 Mm/s .
(i) Calculate the x component of velocity of the third particle
(ii) Calculate the y component of velocity of the third particle
(iii) Calculate the kinetic energy released in the process
I have no idea how to start answering this question... please help!
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Lets start:
(i) the mass of 3rd particle = (17 - 5 - 8.4) x 10^(-27) = 3.6 x 10^(-27)
The total momentum along the X axis was 0. So, after the disintegration it must be 0.
Let v1 be the velocity of the 3rd particle along X axis.
The particle going y direction has no component along x.
So, (8.4 x 10^(-27) x 5.3 x 10^(-3) ) + (3.6 x 10^(-27) x v1) = 0
=> v1 = - 12.37 x 10^(-3) m/s = - 12.37 Mm/s
The minus(-) sign indicates that 3rd particle's X component is in the opposite direction of 1st Particle.
(ii) Same way, if the y component of 3rd particle is v2, then,
(5 x 10^(-27) x 4.2 x 10^(-3) ) + (3.6 x 10^(-27) x v2) = 0
=> v2 = -5.833 x 10^(-3) m/s = -5.833 Mm/s
The minus(-) sign indicates that 3rd particle's Y component is in the opposite direction of 2nd particle.
(iii) 3rd particles actual speed = sqrt((12.37^2) + (5.833^2)) = 13.67 Mm/s = 13.67 x 10^(-3) m/s
So, the total kinetic energy released in the process
= 1/2m1v1^2 + 1/2m2v2^2 + 1/2m3v3^2
= .5 x (8.4 x 10^(-27) x (5.3 x 10^(-3))^2 ) +
.5 x (5 x 10^(-27) x (4.2 x 10^(-3))^2 ) +
.5 x (3.6 x 10^(-27) x (13.67 x 10^(-3))^2)
= 4.984 x 10^(-31) Joule
I think these are the answers if my calculation is not wrong.......
Momentum is conserved. Total momentum = 0 before the disintegration, so total momentum = 0 afterward.
i) Add up the x components of momentum of the other two particles. The 3rd particle has equal and opposite x component so the total is 0. Use momentum = mv to get the velocity.
ii) Add up the y components of momentum of the other two particles. The 3rd particle has equal and opposite y component so the total is 0. Use momentum = mv to get the velocity.
iii) Add up (1/2)mv^2 for all three particles.
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