10.4 Nuclear reactions  (Page 3/19)

As discussed in another chapter, this process occurs due to the weak nuclear force.

As an example, the isotope ${}_{90}^{234}\text{T}\text{h}$ is unstable and decays by ${\beta }^{-}$ emission with a half-life of 24 days. Its decay can be represented as

Since the chemical element with atomic number 91 is protactinium (Pa), we can write the ${\beta }^{-}$ decay of thorium as

The reverse process is also possible: A proton can decay to a neutron by the emission of a positron ( ${\beta }^{+}$ ) and a nearly massless particle called a neutrino    ( v ). This reaction is written as ${}_1^1\text{p}\to {}_0^1\text{n}+{}_{\text{+}1}^0\text{e}\text{+}v.$

The positron ${}_{\text{+}1}^0\text{e}$ is emitted with the neutrino v , and the neutron remains in the nucleus. (Like ${\beta }^{-}$ decay, the positron does not precede the decay but is produced in the decay.) For an isolated proton, this process is impossible because the neutron is heavier than the proton. However, this process is possible within the nucleus because the proton can receive energy from other nucleons for the transition. As an example, the isotope of aluminum ${}_{13}^{26}\text{A}\text{l}$ decays by ${\beta }^{+}$ emission with a half-life of $7.40\times {10}^5\text{y}.$ The decay is written as

The atomic number 12 corresponds to magnesium. Hence,

As a nuclear reaction, positron emission can be written as

The neutrino was not detected in the early experiments on $\beta$ decay. However, the laws of energy and momentum seemed to require such a particle. Later, neutrinos were detected through their interactions with nuclei.

Gamma decay

A nucleus in an excited state can decay to a lower-level state by the emission of a “gamma-ray” photon, and this is known as gamma decay    . This is analogous to de-excitation of an atomic electron. Gamma decay is represented symbolically by

where the asterisk (*) on the nucleus indicates an excited state. In $\gamma$ decay, neither the atomic number nor the mass number changes, so the type of nucleus does not change.

Radioactive decay series

Nuclei with $Z>82$ are unstable and decay naturally. Many of these nuclei have very short lifetimes, so they are not found in nature. Notable exceptions include ${}_{90}^{232}\text{T}\text{h}$ (or Th-232) with a half-life of $1.39\times {10}^{10}$ years, and ${}_{92}^{238}\text{U}$ (or U-238) with a half-life of $7.04\times {10}^8$ years. When a heavy nucleus decays to a lighter one, the lighter daughter nucleus can become the parent nucleus for the next decay, and so on. This process can produce a long series of nuclear decays called a decay series    . The series ends with a stable nucleus.