Question

\(^{210} \mathrm{Pb}\) decays into \(^{206} \mathrm{Pb}\) in a pathway involving two \(\beta\) -emissions followed by an \(\alpha\) -emission. What are the intermediate isotopes? (Section \(3.8)\)

Short answer

The intermediate isotopes are \(^{210}_{83} \mathrm{Bi}\) and \(^{210}_{84} \mathrm{Po}\).

Step-by-step solution

Understanding the Process

The decay process from \(^{210} \text{Pb}\) to \(^{206} \text{Pb}\) involves two \(\beta\)-emissions followed by one \(\alpha\)-emission. \(\beta\)-emission increases the atomic number by 1 without changing the mass number, while \(\alpha\)-emission decreases the atomic number by 2 and the mass number by 4.

First \(\beta\)-Emission

In a \(\beta^-\)-emission, a neutron is converted into a proton, thus increasing the atomic number by 1. Starting with \(^{210}_{82} \text{Pb}\), the first \(\beta^-\)-emission results in \(^{210}_{83} \text{Bi}\).

Second \(\beta\)-Emission

The second \(\beta^-\)-emission again increases the atomic number by 1. Starting with \(^{210}_{83} \text{Bi}\), the second \(\beta^-\)-emission results in \(^{210}_{84} \text{Po}\).

\(\alpha\)-Emission

An \(\alpha\)-emission decreases the atomic number by 2 and the mass number by 4. Starting with \(^{210}_{84} \text{Po}\), the \(\alpha\)-emission results in \(^{206}_{82} \text{Pb}\).

Identifying Intermediate Isotopes

The intermediate isotopes are those formed after the first and second emissions. These isotopes are \(^{210}_{83} \text{Bi}\) and \(^{210}_{84} \text{Po}\).

Key concepts

Beta Emission

Beta emission is a type of nuclear decay where a neutron in an atom's nucleus turns into a proton. During this transformation, an electron, known as a beta particle, is emitted. This process is significant in nuclear physics because it alters the atomic number of the element, transforming it into a different element.

In the example with lead undergoing two beta emissions, each emission increases the atomic number by one. For instance, when lead-210 ( ^{210}_{82} ext{Pb} ) undergoes beta emission, it becomes bismuth-210 ( ^{210}_{83} ext{Bi} ). The mass number remains unchanged during beta emissions, meaning the new element has the same number of nucleons.

• Each beta emission turns a neutron into a proton.
• The atomic number increases by 1.
• Mass number stays the same.

Alpha Emission

Alpha emission is another form of radioactive decay, but it involves the ejection of an alpha particle from the nucleus. An alpha particle consists of 2 protons and 2 neutrons, essentially a helium nucleus. This form of decay leads to a decrease in both the atomic number and the mass number of the original atom.

In the provided example, the element polonium-210 ( ^{210}_{84} ext{Po} ) undergoes alpha emission to form lead-206 ( ^{206}_{82} ext{Pb} ). The emission causes a reduction of the atomic number by 2 and the mass number by 4.

• Alpha particle: 2 protons and 2 neutrons.
• Atomic number decreases by 2.
• Mass number decreases by 4.

Isotope Transformation

Isotope transformation refers to the change of one isotope into another through various nuclear processes, such as beta and alpha emissions. When isotopes transform, they belong to different elements because their atomic numbers change.

For example, the decay path from lead-210 to lead-206 involves transforming through multiple intermediate isotopes. Each transformation means that the atom takes on new properties and becomes a different element as its proton count changes.

• Beta emission results in a new element.
• Alpha emission results in yet another new element.
• Isotope transformation constantly alters the element identity during decay.

Atomic Number Change

Atomic number change is a critical concept in understanding nuclear decay. The atomic number represents the number of protons in an atom's nucleus, and changes to this number result in the transformation of the element.

Beta emissions increase the atomic number since a neutron is converted into an additional proton. Conversely, alpha emissions decrease the atomic number because 2 protons are ejected in an alpha particle.

• With beta emission, atomic number increases by 1.
• With alpha emission, atomic number decreases by 2.
• Understanding these changes helps trace isotope transformations in decay series.