An unstable atomic nucleus of mass 1.74 times 10-26 kg initially at rest disinte

Question

An unstable atomic nucleus of mass 1.74 times 10-26 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.14 times 10-27 kg, moves in the y direction with a speed of 6.00 times 106 m/s. Another particle, of mass 8.46 times 10-27 kg, moves in the x direction with a speed of 4.00 times 106 m/s. Find the velocity of the third particle. Your response is within 10% of the correct value. This may be due to round off error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize round off error. i Your response is within 10% of the correct value. This may be due to round off error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize round off error. j Find the total kinetic energy increase in the process.

Explanation / Answer

By momentum conservation,

M*0 = m1*v1 + m2*v2 +m3*v3

thus, v3 = -(m1v1+m2v2)/m3 = -(5.14*10^-27*6*10^6 j + 8.46*10^-27*4*10^6 i)/(3.8*10^-27) = (8.905i + 8.116j) * 10^6 m/s

Or V3 = 12.05*10^6 m/s

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