Question

The steps below show three of the steps in the radioactive decay chain for \(_{90}^{232}\) Th. The half-life of each isotope is shown below the symbol of the isotope. (a) Identify the type of radioactive decay for each of the steps (i), (ii), and (iii). (b) Which of the isotopes shown has the highest activity? (c) Which of the isotopes shown has the lowest activity? (d) The next step in the decay chain is an alpha emission. What is the next isotope in the chain? [Sections 21.2 and 21.4]

Short answer

(a) The types of radioactive decay are: (i) Alpha decay (ii) Beta decay (iii) Gamma decay (b) The isotope with the highest activity is Ac, with a half-life of 6.25 hours. (c) The isotope with the lowest activity is Th, with a half-life of 14.0 billion years. (d) The next isotope in the decay chain after an alpha emission is \(_{87}^{224}\text{Fr}\), francium.

Step-by-step solution

Identify radioactive decay types for each step

For each step in the decay chain, examine the change in atomic number and mass number to determine the type of decay. There are three types of radioactive decay we need to consider: alpha decay, beta decay, and gamma decay. (i) \(_{90}^{232}\text{Th} \rightarrow _{88}^{228}\text{Ra}\) In this step, the atomic number decreases by 2, and the mass number decreases by 4. This indicates an alpha decay. (ii) \(_{88}^{228}\text{Ra} \rightarrow _{89}^{228}\text{Ac}\) In this step, the atomic number increases by 1, and the mass number remains the same. This indicates a beta decay. (iii) \(_{89}^{228}\text{Ac} \rightarrow _{89}^{228}\text{Th}\) In this step, the atomic number remains the same and the mass number remains the same. This indicates a gamma decay.

Determine isotope with highest activity

To determine the isotope with the highest activity, we can compare their half-lives. The isotope with the shortest half-life will have the highest activity because it is decaying more quickly. Half-lives given: - Th: 14.0 billion years - Ra: 5.75 years - Ac: 6.25 hours Based on these half-lives, isotope Ac has the highest activity.

Determine isotope with lowest activity

To determine the isotope with the lowest activity, we can again compare their half-lives. The isotope with the longest half-life will have the lowest activity because it is decaying less rapidly. Based on the half-lives given, isotope Th has the lowest activity.

Find the next isotope in the decay chain

According to the problem, the next step in the decay chain is an alpha emission. In an alpha emission, the atomic number decreases by 2 and the mass number decreases by 4. We will apply this to the current isotope (Th) to determine the next isotope. Current isotope: \(_{89}^{228}\text{Th}\) Applying alpha emission: - Atomic number: 89 - 2 = 87 - Mass number: 228 - 4 = 224 The next isotope in the decay chain is: \(_{87}^{224}\text{Fr}\), francium.

Key concepts

Alpha Decay

In alpha decay, a radioactive isotope emits an alpha particle, which consists of 2 protons and 2 neutrons. This causes both the atomic number and the mass number of the original atom to decrease.
In other words, alpha decay reduces the atomic number by 2 and the mass number by 4. For instance, when thorium-232 ( _{90}^{232} ext{Th} ightarrow _{88}^{228} ext{Ra} ), undergoes alpha decay, it transforms into radium-228 (₈₈Ra).

Key points to remember about alpha decay include:

• Alpha particles are the same as helium nuclei.
• They have a charge of +2 and are relatively massive compared to other radioactive particles.
• Alpha particles do not penetrate deeply into materials and can be stopped by a sheet of paper or skin.

Beta Decay

Beta decay occurs when a neutron in an atom converts to a proton, accompanied by the ejection of an electron, known as a beta particle.
This process results in the increase of the atomic number by 1 while the mass number remains unchanged.
An example is the decay of radium-228 ( _{88}^{228} ext{Ra} ightarrow _{89}^{228} ext{Ac} ), which results in actinium-228.

Key aspects of beta decay:

• Beta particles are high-energy, high-speed electrons or positrons.
• The new proton increases the atomic number by one but does not affect the mass number.
• Beta particles are more penetrating than alpha particles but can be stopped by materials like aluminum foil.

Gamma Decay

Gamma decay involves the emission of gamma rays, which are high-energy photons. Importantly, gamma decay does not affect the atomic number or the mass number.
It's often a way for the atomic nucleus to release excess energy following other types of decay like alpha or beta decay.
For instance, decay like the conversion from actinium-228 to thorium-228 ( _{89}^{228} ext{Ac} ightarrow _{89}^{228} ext{Th} ) can emit gamma rays.

Characteristics of gamma decay include:

• Gamma rays are the most penetrating type of radiation and require heavy shielding, such as lead, to be blocked effectively.
• Gamma decay usually occurs to release energy after an alpha or beta decay has happened.
• It doesn’t change the amount of protons or neutrons in the nucleus.

Radioactive Isotopes

Radioactive isotopes, also known as radioisotopes, are unstable isotopes of an element that emit radiation as they decay to become more stable.
These isotopes can undergo alpha decay, beta decay, gamma decay, or a combination of these.
For example, in our decay chain, we follow radioactive isotopes such as thorium-232, radium-228, and actinium-228.

Essential points about radioactive isotopes:

• They are used in medical applications, such as cancer treatments and diagnostic imaging.
• The stability or instability of an isotope affects its rate of decay and half-life.
• Radioactive isotopes occur naturally and can also be produced artificially in laboratories.

Half-Life

The half-life of a radioactive isotope is the time it takes for half of the sample to decay.
Half-life helps determine how quickly a radioactive isotope undergoes decay.
In the earlier example, actinium-228 with a half-life of 6.25 hours is more active than thorium-232, which has a half-life of 14 billion years.

Facts about half-life:

• Each isotope has a unique half-life, ranging from fractions of a second to billions of years.
• Half-life is used in various applications, such as carbon dating and nuclear medicine.
• Shorter half-lives mean higher levels of radioactivity, as more decay happens quickly.