SAT Physics Subject Test

Chapter 16 Modern Physics


Natural radioactive decay provides one example of a nuclear reaction. Other examples of nuclear reactions include the bombardment of target nuclei with subatomic particles to artificially induce radioactivity (this is nuclear fission), and the nuclear fusion of small nuclei at extremely high temperatures. In all cases of nuclear reactions that we’ll study, nucleon number and charge must be conserved. To balance nuclear reactions, we write  or for a proton and  for a neutron. Gamma-ray photons can also be produced in nuclear reactions; they have no charge or nucleon number and are represented as .

13. A mercury-198 nucleus is bombarded by a neutron, which causes a nuclear reaction.

What’s the unknown product particle, X?

Here’s How to Crack It

In order to balance the superscripts, we must have 1 + 198 = 197 + A, so A = 2, and the subscripts are balanced if 0 + 80 = 79 + Z, so Z = 1.

Therefore, X must be a deuteron,  (or just d).

Disintegration Energy

Nuclear reactions not only produce new nuclei and other subatomic particles, but also involve the absorption or emission of energy. Nuclear reactions must conserve total energy, so changes in mass are accompanied by changes in energy according to Einstein’s equation ∆E = (∆m)c2.

A general nuclear reaction is written

A + B → C + D + Q

where Q is the disintegration energy.

If Q is positive, the reaction is exothermic and the reaction can occur spontaneously; if Q is negative, the reaction is endothermic and the reaction cannot occur spontaneously. The energy Q is calculated as follows:

Q = [(mA + mB) – (mC + mD)]c2

For spontaneous reactions—ones that liberate energy—most of the energy is revealed as kinetic energy of the least massive product nuclei.