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Chapter 11: Q64E (page 520)

If all the nuclei in a pure sample of uranium-235 were to fission, yielding about 200 MeV each. What is the kinetic energy yield in joules per kilogram of fuel?

Short Answer

Expert verified

Kinetic energy isE=832×1011J/kg

Step by step solution

01

Finding N is the number of uranium atoms.

We need to find the kinetic energy per kilogram of uranium-235 that is used as a fuel. It has about 200 MeV energy.

The total kinetic energy E in this fission process is calculated using the formula:

E=NQ

Here, Q is the energy released in the process, and N is the number of uranium atoms.

First, we will find N is the number of uranium atoms:

mM=N

Here, m is carbon mass, and M is molecule mass.

By substituting numerical values, we have:

N=mMN0=1kg3.9×10-23kgN0=2.6×1024

02

By converting 200 MeV into J.

200MeV=200×1.6×10-13J=320×10-13J

Finally, we can calculate the kinetic energy as:

role="math" localid="1658420259863" E=320×10-13J×2.6×1024E=832×1011J/kg

Therefore, Kinetic energy isE=832×1011J/kg

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Most popular questions from this chapter

Calcium-41 decays by electron capture.

(a) FindQ for the decay.

(b) Show that calcium-41 cannot decay byβ+ emission.

a) For a nucleus of A=220, estimate very roughly how many nucleons would be at the surface.

b) If the binding energy of an interior nucleon due to the internucleon attraction were E1 and if all nucleon were are tightly bound, the total binding energy would beAE1 . Taking into account the different binding of surface nucleons, roughly what would be the total binding energy?

A fusion reaction used to produce neutron beams,

12D+12D→23He+01n

Assuming that the kinetic energy before the fusion is negligible compared with the energy released, calculate the neutronkinetic energy after fusion.

Given initially 40mg of radium-226 (one of the decay products of uranium-238), determine,

(a) The amount that will be left after 500years.

(b) The number of α particles the radium will have emitted during this time, and

(c) The amount of kinetic energy that will have been released.

(d) Find the decay rate of the radium at the end of the 500 year.

The binding energy per nucleon is helium-3 is 2.57 MeV/nucleon. Assuming a nucleon separation of 2.5 fm, determine (a) the gravitational potential energy per nucleon, and (b) the electrostatic energy per proton between the protons. (c) What is the approximate value of the internucleon potential energy per nucleon? (d) D these results agree with the table11.2?
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