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Z A X Z + 1 A X + −1 0 e + v .

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

Watch beta decay occur for a collection of nuclei or for an individual nucleus.

As an example, the isotope 90 234 T h is unstable and decays by β emission with a half-life of 24 days. Its decay can be represented as

90 234 T h 91 234 X + −1 0 e + v .

Since the chemical element with atomic number 91 is protactinium (Pa), we can write the β decay of thorium as

90 234 T h 91 234 P a + −1 0 e + v .

The reverse process is also possible: A proton can decay to a neutron by the emission of a positron ( β + ) and a nearly massless particle called a neutrino    ( v ). This reaction is written as 1 1 p 0 1 n + + 1 0 e + v .

The positron + 1 0 e is emitted with the neutrino v , and the neutron remains in the nucleus. (Like β 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 A l decays by β + emission with a half-life of 7.40 × 10 5 y . The decay is written as

13 26 A l 12 26 X + + 1 0 e + v .

The atomic number 12 corresponds to magnesium. Hence,

13 26 A l 12 26 M g + + 1 0 e + v .

As a nuclear reaction, positron emission can be written as

Z A X Z 1 A X + + 1 0 e + v .

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

Bismuth alpha and beta decay

The 83 211 B i nucleus undergoes both α and β decay. For each case, what is the daughter nucleus?

Strategy

We can use the processes described by [link] and [link] , as well as the Periodic Table, to identify the resulting elements.

Solution

The atomic number and the mass number for the α particle are 2 and 4, respectively. Thus, when a bismuth-211 nucleus emits an α particle, the daughter nucleus has an atomic number of 81 and a mass number of 207. The element with an atomic number of 81 is thallium, so the decay is given by

83 211 B i 81 207 T i + 2 4 H e .

In β decay, the atomic number increases by 1, while the mass number stays the same. The element with an atomic number of 84 is polonium, so the decay is given by

83 211 B i 84 211 P o + −1 0 e + v .
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Check Your Understanding In radioactive beta decay, does the atomic mass number, A , increase or decrease?

Neither; it stays the same.

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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

Z A X * Z A X + γ

where the asterisk (*) on the nucleus indicates an excited state. In γ 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 T h (or Th-232) with a half-life of 1.39 × 10 10 years, and 92 238 U (or U-238) with a half-life of 7.04 × 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.

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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