bei48482_FM

The Qvalueof the nuclear reaction

AB→ CD

is defined as the difference between the rest energies of Aand Band the rest energies

of Cand D:

Q(mAmBmCmD)c^2 (12.27)

If Qis a positive quantity, energy is given off by the reaction. If Qis a negative quantity,

enough kinetic energy KEcmin the center-of-mass system must be provided by the

reacting particles so that KEcmQ0.

Example 12.11

Find the minimum kinetic energy in the laboratory system needed by an alpha particle to cause

the reaction^14 N(, p)^17 O. The masses of^14 N,^4 He,^1 H, and^17 O are respectively 14.00307 u,

4.00260 u, 1.00783 u, and 16.99913 u.

Solution

Since the mases are given in atomic mass units, it is easiest to proceed by finding the mass

difference between reactants and products in the same units and then multiplying by

931.5 MeVu. Thus we have

Q(14.00307 u4.00260 u1.00783 u16.99913 u) (931.5 MeVu)1.20 MeV

The minimum kinetic energy KEcmin the center-of-mass system must therefore be 1.20 MeV in

order for the reaction to occur. From Eq. (12.26) with the alpha particle as A,

KElab KEcm (1.20 MeV)1.54 MeV

The cross section for this reaction is another matter. Because both alpha particles and^14 N nuclei

are positively charged and repel electrically, the greater KEcmis above the threshold of 1.20 MeV,

then the greater the cross section and the more likely the reaction will occur.

12.9 NUCLEAR FISSION

Divide and conquer

As we saw in Sec. 11.4, a lot of binding energy will be released if we can break a large

nucleus into smaller ones. But nuclei are ordinarily not at all easy to split. What we

need is a way to disrupt a heavy nucleus without using more energy than we get back

from the process.

The answer came in 1938 with the realization by Lise Meitner that a nucleus of the

uranium isotope^23592 U undergoes fission when struck by a neutron. It is not the impact

of the neutron that has this effect. Instead, the^23592 U nucleus absorbs the neutron to

become^23692 U, and the new nucleus is so unstable that almost at once it explodes into

two fragments (Fig. 12.17). Later several other heavy nuclides were found to be

fissionable by neutrons in similar processes.

4.0026014.00307



14.00307

mAmB



mB

Qvalue of nuclear

reaction

450 Chapter Twelve

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