Question

Complete this nuclear reaction, and name the decay process: \(? \rightarrow{ }_{5}^{11} \mathrm{~B}+{ }_{-1}^{0} \mathrm{e}\)

Short answer

The complete nuclear reaction is \({ }_{6}^{11}\mathrm{C} \rightarrow { }_{5}^{11}\mathrm{B}+ { }_{-1}^{0}\mathrm{e}\). The decay process is beta-minus decay (\(\beta^{-}\) decay), as a beta particle (electron) is emitted, and the atomic number decreases by 1.

Step-by-step solution

Determine the missing nuclide

In order to do this, we need to conserve both the atomic number (also called proton number) and the mass number (sum of protons and neutrons) on both sides of the equation. The given equation is: \(?\rightarrow { }_{5}^{11}\mathrm{B} + { }_{-1}^{0}\mathrm{e}\) To conserve the atomic numbers: \(Z = 5 - (-1) = 6\) To conserve the mass numbers: \(A = 11-0 = 11\) The missing nuclide has atomic number 6 and mass number 11. According to the periodic table, this corresponds to Carbon-11: \( { }_{6}^{11}\mathrm{C}\). Now, we write the complete reaction: \({ }_{6}^{11}\mathrm{C} \rightarrow { }_{5}^{11}\mathrm{B}+ { }_{-1}^{0}\mathrm{e}\)

Identify the decay process

In this reaction, a Carbon-11 nucleus transforms into a Boron-11 nucleus, and an electron is emitted. This process is called beta decay because a beta particle (electron) is released. More specifically, this is a case of beta-minus decay (\(\beta^{-}\) decay), as it involves the emission of an electron and a decrease in the atomic number of the parent nucleus. Thus, the decay process in the given nuclear reaction is called beta-minus decay (\(\beta^{-}\) decay).

Key concepts

Nuclear Reaction

A nuclear reaction involves the change of an atom's nucleus, usually causing the transformation of elements or isotopes. In the context of beta-minus decay, one type of nuclear reaction, a neutron within the nucleus is transformed into a proton, while a beta particle, which is an electron, and an antineutrino are emitted. This results in a change in the atomic number of the atom, but not its mass number, as the total number of protons and neutrons remains constant. Nuclear reactions are different from chemical reactions; the latter involve only the electrons surrounding the nucleus and typically do not result in the transformation of elements.

Atomic Number Conservation

The law of conservation of atomic number states that in any nuclear reaction, the sum of atomic numbers before and after the reaction must remain equal. Atomic number, represented by the symbol 'Z', is the number of protons in the nucleus of an atom and determines the identity of the element. In beta-minus decay, when a neutron gets converted to a proton, the atomic number increases by one. However, the emitted beta particle, which is an electron, has an atomic number of -1. Thus, when it is emitted, it balances the increase in the atomic number of the nucleus, ensuring the overall conservation.

Mass Number Conservation

Similarly, the conservation of mass number is key in nuclear reactions. The mass number 'A' is the total number of protons and neutrons in an atom's nucleus. In beta-minus decay, although a neutron in the nucleus changes into a proton and an electron, the total count of protons plus neutrons remains unchanged because the proton remains in the nucleus and the neutron's mass is effectively replaced by the proton's mass. Therefore, the mass number before and after the decay remains the same, satisfying the principle of mass number conservation.

Beta Particle Emission

Beta particle emission is a fundamental aspect of beta-minus decay. This emission involves an electron, which is negated from the atomic structure, reducing the neutron to a proton. The release of a beta particle signifies a transformation within the nucleus and is associated with weak nuclear force, one of the four fundamental forces of nature. Beta particles have a significant application in both medical treatments, like radiotherapy, and research, due to their penetrative properties and the ability to study weak force interactions.