Question 14.6: Calculate the energy released by a nucleus of uranium-235 if......

The masses of the various particles involved are shown in the table below.

We can sum the appropriate particle masses to find the masses of the reactants and the products.

Now we subtract to find the mass defect.

Analyze Your Answer The first thing we notice about our answer is that it is negative. Does this make sense? Notice that we have calculated \Delta m as the mass of the products minus the mass of the reactants, in keeping with the conventions we used in our discussions of thermodynamics. This means that the resulting value, and the corresponding energy, will also follow the thermodynamic sign conventions. So the fact that we have a negative energy confirms that this is the amount of energy released in the fission reaction, as expected. How can we assess the magnitude of our answer? First, keep in mind that this is the energy released by the fission of a single atom of { }^{235} U. Then remember that we expect a nuclear reaction to release much more energy than an ordinary chemical reaction. We know that the energy released in an exothermic chemical reaction is typically on the order of hundreds or perhaps thousands of kJ/mol. So we might convert our answer to kJ/mol to make a comparison. The result above corresponds to 10^{10} kJ/mol. This is clearly much larger than what would be seen in any chemical reaction, so it seems plausible for the nuclear reaction considered here.

Check Your Understanding A single neutron can also induce the fission of { }^{235} U to produce { }^{90} Sr and { }^{143} Xe. Calculate the energy released when 1.00 kg of { }^{235} U undergoes this reaction. The experimentally determined masses are m_{ Sr }=89.9077376\ u, m_{ Xe }=142.9348900\ u.