An unstable atomic nucleus of mass 1.68 10-26 kg initially at rest disintegrates
ID: 1445502 • Letter: A
Question
An unstable atomic nucleus of mass 1.68 10-26 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.02 10-27 kg, moves in the y direction with a speed of 6.00 106 m/s. Another particle, of mass 8.44 10-27 kg, moves in the x direction with a speed of 4.00 10^6 m/s.
An unstable atomic nucleus of mass 1.68 x 1026 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.02x1027 kg, moves in the y direction with a speed of 6.00 x 106 m/s. Another particle, of mass 8.44 x 1027 kg, moves in the x direction with a speed of 4.00 x 106 m/s. (a) Find the velocity of the third particle. 10064516. Your response differs from the correct answer by more than 10%. Double check your calculations.) m/s (b) Find the total kinetic energy increase in the process Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.Explanation / Answer
M = mass of nucles = 1.68*10-26 kg
u = initial velocity of nucles = 0 m/s
m1 = mass of 1st particle = 5.02*10-27 kg
V1 = velocity of 1st particle = 6*106 m/s
m2 = mass of 2nd particle = 8.44*10-27 kg
V2 = velocity of 2nd particle = 4*106 m/s
m3 = 3rd particle mass = M - m1 - m2
m3 = 3.34 *10-27 kg
V3 = 3rd particle velocity = ?
conservation of momentum in x- direction
M*ux = m1*V1x + m2*V2x + m3*V3x
0 = 0 + m2*V2x + m3*V3x
V3x = - m2*V2x / m3
= - 8.44*10-27*4*106 / 3.34*10-27
= - 10.1*106 m/s
momentum in y - direction
M*uy = m1*V1y + m2*V2y + m3*V3y
0 = m1*V1y + 0 + m3*V3y
V3y = - m1*V1y / m3
= - 5.02*10-27 *6*106 / 3.34*10-27
= - 9*106 m/s
V3 = - 10.1*106 (i) m/s - 9*106 (j) m/s
magnitude of V3 = ( ( -10.1*106)2 + ( -9*106 )2)1/2
V3 = 1.83*1014 m/s
B) increase in K.E = K.E_final
= (1/2)*[m1*V12 + m2*V22 + m3*V32]
(1/2)* [ 5.02*10-27 * ( 6*106)2 + 8.44*10-27 * ( 4*106)2 + 3.34*10-27* ( 1.83*1014)2]
= 55.9 J
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