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Professional Application: One of the waste products of a
Chapter 8, Problem 39(choose chapter or problem)
Problem 39PE
Professional Application:
One of the waste products of a nuclear reactor is plutonium-239 (239Pu) . This nucleus is radioactive and decays by splitting into a helium-4 nucleus and a uranium-235 nucleus (4He + 235U), the latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is 8.40×10– 13 J and is entirely converted to kinetic energy of the helium and uranium nuclei. The mass of the helium nucleus is 6.68×10–27 kg , while that of the uranium is 3.92×10–25 kg (note that the ratio of the masses is 4 to 235). (a) Calculate the velocities of the two nuclei, assuming the plutonium nucleus is originally at rest. (b) How much kinetic energy does each nucleus carry away? Note that the data given here are accurate to three digits only.
Questions & Answers
QUESTION:
Problem 39PE
Professional Application:
One of the waste products of a nuclear reactor is plutonium-239 (239Pu) . This nucleus is radioactive and decays by splitting into a helium-4 nucleus and a uranium-235 nucleus (4He + 235U), the latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is 8.40×10– 13 J and is entirely converted to kinetic energy of the helium and uranium nuclei. The mass of the helium nucleus is 6.68×10–27 kg , while that of the uranium is 3.92×10–25 kg (note that the ratio of the masses is 4 to 235). (a) Calculate the velocities of the two nuclei, assuming the plutonium nucleus is originally at rest. (b) How much kinetic energy does each nucleus carry away? Note that the data given here are accurate to three digits only.
ANSWER:
Solution 39PE :
Here the goal is to determine the velocities of the decaying particles.
Step 1 of 5:
Initially the plutonium nucleus was at rest, so the linear momentum was zero.
After the decay, two particles came out of it which are nucleus and
nucleus.
The mass of the nucleus is,
.
The mass of the nucleus is,
.
The total energy emitted in the decay is, which got converted into the kinetic energy of the decaying particles.
a)