A 232 Th (thorium) nucleus at rest decays to a 228 Ra (radon) nucleus with the e
ID: 1894353 • Letter: A
Question
A 232 Th (thorium) nucleus at rest decays to a 228 Ra (radon) nucleus with the emission of an alpha particle. The total kinetic energy of the decay fragments is 6.54 x 10^-13 J. The radon nucleus has a mass of 3.6 X 10^-25 KG and the alpha particle has a mass of 6.64 X10^-27KG. The radon nuclues has a velocity of 250680.3047m/s.A) What is the velocity of the alpha particle?
B) What is the kinetic energy of the alpha particle?
The total kinetic energy it gives you isnt needed is it? if not then what is a mthod you could use to involve the total kinetic energy
Explanation / Answer
We need to conserve momentum in this totally inelastic collision. (Breaking apart or clumping together are totally inelastic "collisions." Kinetic energy doesn't have a direction. We have a lot of good information to solve this. For conservation of momentum, we have M radon* V radon = M alpha*V alpha (in opposite directions) V alpha = M radon* V radon/ M alpha = 1.36E+07m/s just like you (this is really fast) KE of alpha = 1/2 M alpha * V alpha^2 = 6.13E-13 J, just like you This is most of the KE. This makes sense since KE has v^2 Let's check KE of Radon = 1/2 M radon*Vradon = 1.13E-14J total = 6.25 x 10^-13J Hmmm... are relativistic effects coming into play? Does mass increase as we approach the speed of light? Yes! We need to use the relativistic mass. Let's find the real KE 6.54 E-13J - KE radon = KE alpha 6.54 E-13J - 1.13E-14J = 6.43E-13 J This is the correct answer to (B) The radon is going so slow that relativistic effects aren't a factor for it. So the mass of the alpha particle is going to be larger.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.