Question

Predict the type of radioactive decay process for the following radionuclides: \((\mathbf{a})_{5}^{8} \mathrm{B}\) \((\mathbf{b})_{29}^{68} \mathrm{Cu},(\mathbf{c})\) phosphorus-32 \((\mathbf{d}),\)chlorine-39.

Short answer

The predicted types of radioactive decay processes for the given radionuclides are: a) \(_{5}^{8} \mathrm{B}\): Beta-plus decay or electron capture. b) \(_{29}^{68} \mathrm{Cu}\): Beta-minus decay. c) Phosphorus-32: Beta-minus decay. d) Chlorine-39: Beta-minus decay.

Step-by-step solution

Determine atomic number, mass number, and neutron number

For this radionuclide, Z=5 (boron), A=8, and N=A-Z=8-5=3.

Calculate neutron-proton ratio

The neutron-proton ratio is N/Z=3/5=0.6, which is low, implying that we might expect beta-plus decay or electron capture for this radionuclide. \(\mathrm{b}) \,_{29}^{68} \mathrm{Cu}\)

Determine atomic number, mass number, and neutron number

For this radionuclide, Z=29 (copper), A=68, and N=A-Z=68-29=39.

Calculate neutron-proton ratio

The neutron-proton ratio is N/Z=39/29=1.34, which is high, implying that we might expect beta-minus decay for this radionuclide. \(\mathrm{c})\) phosphorus-32

Determine atomic number, mass number, and neutron number

For this radionuclide, Z=15 (phosphorus), A=32, and N=A-Z=32-15=17.

Calculate neutron-proton ratio

The neutron-proton ratio is N/Z=17/15=1.13, which is high, implying that we might expect beta-minus decay for this radionuclide. \(\mathrm{d}),\)chlorine-39

Determine atomic number, mass number, and neutron number

For this radionuclide, Z=17 (chlorine), A=39, and N=A-Z=39-17=22.

Calculate neutron-proton ratio

The neutron-proton ratio is N/Z=22/17=1.29, which is high, implying that we might expect beta-minus decay for this radionuclide. The predicted types of radioactive decay processes for each radionuclide are as follows: a) Beta-plus decay or electron capture b) Beta-minus decay c) Beta-minus decay d) Beta-minus decay

Key concepts

Neutron-Proton Ratio

In the realm of nuclear physics, the neutron-proton ratio is a crucial determinant for the stability of an atom's nucleus. It essentially tells us how many neutrons exist in the nucleus for every proton.

Atoms strive for a balanced existence, and certain neutron-to-proton ratios provide that balance, leading to a stable nucleus. On the flip side, if the ratio is too low or too high, the nucleus becomes unstable and will likely undergo radioactive decay to reach stability. For lighter elements (like Boron from our example), a 1:1 ratio close to unity is often a sign of stability, but as we move to heavier elements, a slightly greater number of neutrons is needed to maintain stability because of the increased repulsion between the protons.

Beta-Plus Decay

One form of nuclear alchemy is beta-plus decay, also known as positron emission. When a nucleus has too few neutrons compared to protons, it might choose this path to right the balance. A proton in the nucleus is transformed into a neutron, releasing a positron, which is the antimatter twin of an electron, hence the 'plus' in beta-plus.

In the process, an element's atomic number drops by one, but its atomic mass remains the same. Consider our Boron example: a beta-plus decay would transform it into beryllium, with one less proton but the same mass number of 8.

Beta-Minus Decay

Beta-minus decay is like the mirror image of beta-plus decay. This time, a nucleus with an overabundance of neutrons (and remember, an imbalanced neutron-proton ratio is a no-no for atomic stability) converts a neutron into a proton. Along with this conversion, an electron, also known as a beta particle, is emitted — thus 'minus' for the electron's negative charge.

As a result, the atomic number increases by one — here's looking at copper in our exercise becoming zinc — but the mass number stays constant, considering electrons have an insignificantly small mass compared to protons or neutrons.

Electron Capture

Sometimes, instead of emitting a positron, an unstable nucleus with too many protons will pull an electron from its orbit right into the nucleus — a process fittingly named electron capture. This troublesome electron joins forces with a proton, converting it into a neutron and emitting a neutrino in the process.

The change again reduces the atomic number by one but keeps the mass number intact. For example, if Boron were to undergo electron capture, it too would become stable Beryllium, similar to the beta-plus decay but through a different pathway. In a cosmic game of balance, nature always finds a way toll the bell of equilibrium.

Radionuclide Identification

The art of radionuclide identification involves unmasking the identity of radioactive isotopes and predicting their decay pathways. Every radionuclide has its nuclear signature: atomic number, mass number, and the neutron-proton ratio, which clues us into its current state and future metamorphoses. By understanding the neutron-proton ratio, scientists can anticipate whether a radionuclide will undergo beta-plus decay, beta-minus decay, or electron capture — critical for everything from nuclear medicine to astrophysics.

Every step in predicting radioactive decay, like the ones in our exercise, enhances our grasp of these nuclear transformations, aiding us in aspects as diverse as medical imaging and tracking cosmic events.