Question

Predict the type of radioactive decay process for the following radionuclides: (a) ${}_5^8\mathrm{B}$, (b) ${}_{29}^{68}\mathrm{Cu}$, (c) phosphorus-32, (d) chlorine-39. 21.20 Each of the following nuclei undergoes either beta decay or positron emission. Predict the type of emission for each: (a) tritium, ${}_1^3\mathrm{H}$, (b) ${}_{38}^{89}\mathrm{Sr}$, (c) iodine-120, (d) silver-102.

Short answer

The predicted decay types for the given radionuclides are: (a) ${}_5^8\text{B}$: Positron emission (${\beta }^{+}$) (b) ${}_{29}^{68}\text{Cu}$: Beta decay (${\beta }^{-}$) (c) Phosphorus-32: Beta decay (${\beta }^{-}$) (d) Chlorine-39: Beta decay (${\beta }^{-}$) For the second part of the exercise, the predicted type of emission for each is: (a) Tritium, ${}_1^3\text{H}$: Beta decay (${\beta }^{-}$) (b) ${}_{38}^{89}\text{Sr}$: Positron emission (${\beta }^{+}$) (c) Iodine-120: Positron emission (${\beta }^{+}$) (d) Silver-102: Positron emission (${\beta }^{+}$)

Step-by-step solution

Determine the isotope's stability

There are 5 protons and 3 neutrons in this isotope, meaning it has too many protons compared to neutrons. Therefore, it will undergo a decay to convert one of the protons into a neutron.

Predict the decay type

As the isotope has too many protons, it is likely to undergo positron emission, which will convert a proton to a neutron and decrease the atomic number by 1. The predicted decay type is positron emission (${\beta }^{+}$). (b) ${}_{29}^{68}\text{Cu}$

Determine the isotope's stability

This isotope has 29 protons and 39 neutrons. Since Cu-63 and Cu-65 are the stable isotopes of copper, this isotope has too many neutrons compared to protons.

Predict the decay type

As this isotope has too many neutrons compared to protons, it is likely to undergo beta decay. This would convert a neutron to a proton, thereby increasing the atomic number by 1. The predicted decay type is beta decay (${\beta }^{-}$). (c) Phosphorus-32

Determine the isotope's stability

This isotope has 15 protons and 17 neutrons. The most stable isotope of phosphorus is P-31, so this isotope has one too many neutrons compared to protons.

Predict the decay type

With too many neutrons, this isotope is predicted to undergo beta decay, converting a neutron to a proton and increasing the atomic number by 1. The predicted decay type is beta decay (${\beta }^{-}$). (d) Chlorine-39

Determine the isotope's stability

This isotope has 17 protons and 22 neutrons. The stable isotopes of chlorine are Cl-35 and Cl-37, which means this isotope has too many neutrons compared to protons.

Predict the decay type

Having too many neutrons, this isotope is likely to undergo beta decay, converting a neutron to a proton and therefore increasing the atomic number by 1. The predicted decay type is beta decay (${\beta }^{-}$). Now, let's predict the type of emission for the second part of the exercise: (a) Tritium, ${}_1^3\text{H}$

Determine the isotope's stability

This isotope has 1 proton and 2 neutrons, while the stable isotope of hydrogen is H-1, which means this isotope has too many neutrons compared to protons.

Predict the decay type

Since tritium has too many neutrons, it is predicted to undergo beta decay, converting a neutron to a proton and hence increasing the atomic number by 1. The predicted decay type is beta decay (${\beta }^{-}$). (b) ${}_{38}^{89}\text{Sr}$

Determine the isotope's stability

This isotope has 38 protons and 51 neutrons. The stable isotopes of strontium are Sr-88, Sr-87, Sr-86, and Sr-84, which means this isotope has too many protons compared to neutrons.

Predict the decay type

As this isotope has too many protons, it is likely to undergo positron emission, converting a proton to a neutron and decreasing the atomic number by 1. The predicted decay type is positron emission (${\beta }^{+}$). (c) Iodine-120

Determine the isotope's stability

This isotope has 53 protons and 67 neutrons. Since the stable isotopes of iodine are around I-127, iodine-120 has too few neutrons compared to protons.

Predict the decay type

With too few neutrons and too many protons, the isotope is expected to undergo positron emission, converting a proton to a neutron and decreasing the atomic number by 1. The predicted decay type is positron emission (${\beta }^{+}$). (d) Silver-102

Determine the isotope's stability

This isotope has 47 protons and 55 neutrons. The stable isotopes of silver are Ag-107 and Ag-109, which means this isotope has too few neutrons compared to protons.

Predict the decay type

Since this isotope has too few neutrons and too many protons, it is predicted to undergo positron emission, converting a proton to a neutron and decreasing the atomic number by 1. The predicted decay type is positron emission (${\beta }^{+}$).

Key concepts

Beta Decay

Beta decay is a common type of radioactive decay where an unstable nucleus transforms, releasing energy in the form of radiation. This process involves a neutron in the nucleus changing into a proton and emitting a beta particle, which is an electron. Let's examine how this affects the atom:

• The atomic number of the element increases by one because a neutron changes into a proton. This transformation turns the atom into a different element.
• The mass number, however, remains unchanged because the transformation is within the nucleus and doesn't add or remove an overall nucleon.
• The beta particle released is the electron. Although small, it carries away kinetic energy, reducing the overall energy of the nucleus and making it more stable.

Through beta decay, elements like phosphorus-32 with excess neutrons convert them into protons, thereby moving closer to a stable state. Elements with too many neutrons relative to protons can undergo beta decay to reach a more balanced and stable configuration.

Positron Emission

Positron emission is another form of radioactive decay, which occurs when a proton in an unstable nucleus transforms into a neutron. This process emits a positron, which is the antimatter counterpart of an electron. Here’s how positron emission functions:

• Since a proton is converting into a neutron, the atomic number of the element decreases by one. This results in the transformation of the atom into a new element.
• The mass number remains the same as no nucleons are lost; only their composition has changed within the nucleus.
• The positron emitted is similar to an electron but with a positive charge. When emitted, it can encounter electrons, leading to mutual annihilation and releasing energy in the form of gamma radiation.

Isotopes that exhibit an excess of protons—like ${}_5^{8}extB$—may undergo positron emission to convert one of these protons into a neutron, stabilizing the atomic composition of the element. The release of the positron helps in balancing the overall charge and energy of the atom.

Isotope Stability

Isotope stability refers to how likely an isotope of an element will remain unchanged or undergo radioactive decay over time. Stability is influenced by the ratio of neutrons to protons in the nucleus. Key factors for understanding isotope stability include:

• An ideal balance of neutrons and protons fosters a stable nucleus. The strong nuclear forces must adequately counteract the repulsion between positively charged protons.
• Isotopes that deviate significantly from the neutron-to-proton ratio typical for stability are likely to undergo forms of radioactive decay such as beta decay or positron emission.
• Radioactive isotopes, which are less stable, will transform over time through these decay processes until a stable isotope or element is formed.

For example, isotopes like ${}_1^{3}extH$ (tritium) highlight the principles of isotope stability. Tritium has more neutrons compared to the stable hydrogen-1, leading it to undergo beta decay over time. Understanding which isotopes are stable gives chemists and physicists insight into the behavior of elements under various conditions and helps in tailoring isotopes for practical applications such as medical imaging, radiometric dating, and nuclear power generation.