Problem 43 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of \(\alpha\) and \(\beta\) particle emitted in the nuclear reaction \({ }^{228} \mathrm{Th}_{90} \longrightarrow{ }^{212} \mathrm{Bi}_{83}\) are (a) \(4 \alpha\) and \(1 \beta\) (b) \(3 \alpha\) and \(7 \beta\) (c) \(8 \alpha\) and \(1 \beta\) (d) \(4 \alpha\) and \(7 \beta\)

Step-by-Step Solution

Answer

The number of emitted particles are 4 \( \alpha \) and 1 \( \beta \).

Step 1: Understanding the Problem

We are given a nuclear reaction from Thorium-228 to Bismuth-212. The question asks for the numbers of \( \alpha \) and \( \beta \) particles emitted during this transition.

Step 2: Balancing the Mass Number

\( \alpha \) decay reduces the mass number by 4 (since an \( \alpha \) particle has 2 protons and 2 neutrons), and \( \beta \) decay has no effect on the mass number. Initially, Thorium-228 has a mass number of 228, and Bismuth-212 has a mass number of 212. Calculate the decrease in mass number: \[ 228 - 212 = 16 \]The reduction corresponds to the emission of \( \frac{16}{4} = 4 \alpha \) particles.

Step 3: Balancing the Atomic Number

\( \alpha \) decay decreases the atomic number by 2, whereas \( \beta \) decay increases it by 1. Initially, Thorium has an atomic number of 90, and Bismuth has an atomic number of 83. Calculate the change: \[ 90 - 83 = 7 \]For 4 \( \alpha \) decays, the atomic number is reduced by \( 4 \times 2 = 8 \). To achieve a total reduction of 7, \( 1 \beta \) particle must be emitted to increase the atomic number by 1 (back from 82 to 83 after \( \alpha \) decays).

Step 4: Solution Verification

After calculating that 4 \( \alpha \) decays account for a reduction in both mass and atomic numbers, and adding 1 \( \beta \) decay to adjust the atomic number back up to 83, our solution is verified.Thus, 4 \( \alpha \) particles and 1 \( \beta \) particle are emitted.

Key Concepts

Alpha Decay

In nuclear reactions, alpha decay is a type of radioactive decay where an unstable nucleus releases an alpha particle. This particle consists of 2 protons and 2 neutrons, exactly the same as a helium nucleus. Therefore, when an alpha particle is emitted, the original atom loses a part of its nucleus.

• Alpha decay decreases the atomic number by 2 because it loses 2 protons.
• Similarly, it reduces the mass number by 4 since 2 protons and 2 neutrons are let go.

Alpha decay is common among heavy elements, like uranium and thorium. These elements go through alpha decay to become lighter and reach stable forms. The reaction from Thorium-228 to Bismuth-212 described in the exercise is a clear example - a natural process where the mass becomes progressively smaller over several steps of decay.

Beta Decay

Beta decay is another form of radioactive transformation. However, unlike alpha decay, beta decay doesn't involve large particles like helium nuclei. Instead, it involves the transformation within the atom's nucleus itself.
There are two types of beta decay: beta minus (β⁻) and beta plus (β⁺) decay. In beta minus decay, a neutron is converted into a proton and an electron (the beta particle), while in beta plus decay, a proton is converted into a neutron and a positron.

• Beta decay changes the atomic number by 1.
• It does not impact the mass number because the mass of the neutron and proton is nearly identical.

In the exercise example, beta decay helps adjust the atomic number upwards by 1 to balance the subtraction caused by alpha decays. This is critical for elements to reach stability after shedding protons and neutrons.

Atomic Number

The atomic number is fundamental in defining an element. It directly corresponds to the number of protons in the nucleus of an atom. Each element on the periodic table has a unique atomic number, which indicates the number of protons as well as the identity of the element.

• Atomic number dictates the element's position on the periodic table.
• It determines the chemical properties of the element.

During a nuclear reaction such as alpha or beta decay, the atomic number can change. Alpha decay decreases it by 2 (due to losing protons), whereas beta decay can increase it by 1 (if gaining a proton). In the exercise, the transition from Thorium (atomic number 90) to Bismuth (atomic number 83) involves changes in the atomic number by multiple alpha and beta decays.

Mass Number

The mass number is another key feature of an atom, originally stemming from the sum of its protons and neutrons. These components are located in the atom’s nucleus, thus contributing significantly to its total mass.

• Mass number = Number of protons + Number of neutrons.
• It helps to understand isotopes, which differ only in their neutron count, not protons.

In the context of the exercise, alpha decay is central, reducing the mass number of a nucleus by 4 with each decay event. While beta decay does not influence the mass number, it plays a major role in stabilizing elements through changes in atomic number alone. Transitioning from Thorium-228 to Bismuth-212 shows the significance of mass number adjustments through these nuclear reactions.