Question

The number of \(\alpha\) and \(\beta\) particle emitted in the nuclear reaction \({ }^{228} \mathrm{Th}_{90} \longrightarrow{ }^{212} \mathrm{Bi}_{\mathrm{g} 3}\) are (a) \(4 \alpha\) and \(1 \beta\) (b) \(3 \alpha\) and \(7 \beta\) (c) \(8 \alpha\) and \(1 \beta\) (d) \(4 \alpha\) and \(7 \beta\)

Short answer

(a) 4 \(\alpha\) and 1 \(\beta\).

Step-by-step solution

Understand the Problem

We need to find out how many alpha (\(\alpha\)) and beta (\(\beta\)) particles are emitted when Thorium-228 decays into Bismuth-212 (\( ^{228}_{90} \mathrm{Th} \rightarrow ^{212}_{83} \mathrm{Bi} \)). Each alpha particle decreases the atomic number by 2 and the mass number by 4. Each beta particle changes a neutron into a proton, increasing the atomic number by 1.

Calculate Alpha Particle Emissions

The initial nucleus \(^{228}_{90}\mathrm{Th}\) has a mass number of 228 and atomic number of 90, while the final nucleus \(^{212}_{83}\mathrm{Bi}\) has a mass number of 212 and atomic number of 83.\(228 - 212 = 16\) units are reduced in the mass number. Since each \(\alpha\) particle reduces the mass number by 4, the number of \(\alpha\) particles is \(\frac{16}{4} = 4\).

Calculate Beta Particle Emissions

Considering the atomic number, start at 90 and end at 83. Emitting 4 \(\alpha\) particles reduces the atomic number by \(4 \times 2 = 8\), resulting in \(90 - 8 = 82\). Since the final atomic number is 83, one \(\beta\) particle is emitted to increase the atomic number from 82 to 83.

Determine Answer

The process emits 4 \(\alpha\) particles and 1 \(\beta\) particle. Compare with given options: the correct answer is (a) \(4 \alpha\) and \(1 \beta\).

Key concepts

Alpha Particle Emissions

In nuclear reactions, alpha particle emissions involve the release of an alpha particle from an unstable atom. An alpha particle is made up of 2 protons and 2 neutrons, symbolized as \( \alpha \) or \( ^{4}_{2}He \). When an alpha particle is emitted, the mass number of the atom decreases by 4, and the atomic number decreases by 2.

Understanding alpha particle emissions is crucial as it helps explain the process of element decay in heavy, unstable nuclei.
Alpha particle emissions can be observed in elements like Thorium and Uranium, where the large difference between the number of protons and neutrons makes the nuclei unstable.

For instance, in the decay of Thorium-228, four alpha particles are emitted, which reduces the mass number from 228 to 212. This emission also decreases the atomic number from 90 to 82 initially before other decay processes, such as beta emissions, take over.
- **Key Points**
- Each alpha particle emission reduces the mass number by 4.
- Each emission results in a reduction of the atomic number by 2.

Beta Particle Emissions

Beta particles are high-energy, high-speed electrons or positrons that are emitted by certain types of radioactive nuclei such as Strontium-90 and Carbon-14. This process is known as beta decay.

In contrast to alpha decay, beta particle emissions increase the atomic number of the isotope by 1 because a neutron in the nucleus is transformed into a proton and an electron (the beta particle).

Beta decay doesn't change the mass number, but it alters the atomic structure of the element, resulting in the formation of a different element. - **Example in Nuclear Reactions**
In the reaction of \(^{228}_{90} \mathrm{Th} \rightarrow ^{212}_{83} \mathrm{Bi}\), one beta particle is emitted to convert a neutron into a proton after four alpha particles have been emitted.

This is crucial as it increases the atomic number from 82 (as reduced by alpha emissions) to 83, maintaining the stability and transitioning to the element Bismuth.

**Key Takeaways**

• Each beta emission increases the atomic number by 1.
• No change occurs to the mass number during beta decay.
• Beta decay helps to balance neutron-to-proton ratios in atomic nuclei.

Element Decay

Element decay refers to the process in which an unstable atomic nucleus loses energy by emitting radiation such as alpha or beta particles. This process results in the transformation of elements into other elements or isotopes.

The initial unstable nucleus is known as the parent nucleus, and the finished or transformed nucleus is referred to as the daughter nucleus.

**Significance of Element Decay**

• Element decay is vital for understanding radioactive series found in nature and nuclear reactions in power generation.
• The decay process is responsible for the creation of new elements and isotopes fundamentally altering chemical properties.

In the specific case of \(^{228}_{90} \mathrm{Th} \rightarrow ^{212}_{83} \mathrm{Bi}\), Thorium loses stability due to excess neutrons and undergoes four alpha decays and one beta decay. This results in a stable isotope of Bismuth.

These transformations not only bring about a change in the physical characteristics of the element but also alter its place in the periodic table. This understanding helps in applications ranging from medicine to archeology and acts as a profound mechanism in the study of cosmology.

**Key Points to Remember**

• Decay transforms an unstable element into a stable one.
• It involves a sequence of emissions that change the atomic structure.
• The process is predictable and follows specific decay schemes.