Question

In the following disintegration series \({ }_{92} \mathrm{U}^{238} \rightarrow^{\alpha} \mathrm{x} \rightarrow^{\beta-}{ } \mathrm{Z} \mathrm{y}^{\mathrm{A}}\) The value of \(Z\) and \(A\) respectively will be (A) 90,234 (B) 92,236 (C) 88,234 (D) 91,234

Short answer

The values of Z and A for the final product in the disintegration series are 91 and 234, respectively. The correct answer is (D) 91,234.

Step-by-step solution

Analyzing alpha decay process

In alpha decay, an unstable nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. This means that the atomic number (Z) decreases by 2, and the mass number (A) decreases by 4. Given the decay series: \({ }_{92} \mathrm{U}^{238} \rightarrow^{\alpha} \mathrm{x}\) Using the conservation of nucleon number: Z: \(92 - 2 = 90\) A: \(238 - 4 = 234\) The element x after the alpha decay has an atomic number of 90 and a mass number of 234.

Analyzing the beta-minus decay process

In beta-minus decay, a neutron in the nucleus gets converted to a proton, and an electron (beta particle) is emitted. This means that the atomic number (Z) increases by 1, but the mass number (A) remains the same. Given the decay series: \( \mathrm{x} \rightarrow^{\beta-} { } \mathrm{Z} \mathrm{y}^{\mathrm{A}} \) Applying the conservation of nucleon number to this decay: Z: \(90 + 1 = 91\) A: 234 (remains the same) The final product has an atomic number of 91 and a mass number of 234.

Matching with the given options

Comparing our results with the given options, we find that the correct answer is: (D) 91,234

Key concepts

Alpha Decay

Alpha decay is a fundamental nuclear process where an unstable nucleus lets go of an alpha particle. An alpha particle is made up of 2 protons and 2 neutrons. What this means is that the

• Atomic number (Z) will decrease by 2.
• Mass number (A) will decrease by 4.

For example, if Uranium-238, denoted as \({}_{92}U^{238}\), goes through alpha decay, it's like it loses a small box containing 2 protons and 2 neutrons. This results in a new element with:

• Atomic number: 92 - 2 = 90.
• Mass number: 238 - 4 = 234.

The new element formed after this decay in our scenario becomes \({}_{90}Th^{234}\). By acknowledging these changes, you can predict the element formed after alpha decay.

Beta Decay

Beta decay is another type of nuclear transformation, but it's quite different from alpha decay. In this process, a neutron inside the nucleus converts into a proton. At this time, it emits a beta particle, which is essentially an electron that speeds away from the atom.

When beta-minus decay happens:

• The atomic number (Z) increases by 1.
• The mass number (A) remains the same.

Returning to our uranium series, when the element \({}_{90}Th^{234}\) undergoes beta-minus decay, its atomic number rises by 1, hence becoming:

• Atomic number: 90 + 1 = 91.
• Mass number: stays 234.

Thus, the final product after beta-minus decay in this series is \({}_{91}Pa^{234}\). It's essential to recognize the transformation process to understand radioactive decay pathways.

Atomic Number

The atomic number, represented by the symbol Z, is a crucial identifier for any chemical element. It signifies the number of protons present in the nucleus of an atom.

• Each element has a unique atomic number, making it different from others.
• The periodic table is arranged according to an increasing atomic number.

In nuclear decay scenarios like our exercise, the atomic number effectively changes, helping predict the element transformation. For example:

• In alpha decay, the atomic number decreases by 2.
• In beta-minus decay, the atomic number grows by 1.

Understanding the atomic number's role will help you grasp which element arises after a nuclear reaction.

Mass Number

The mass number, also known by its symbol A, is a fundamental property of an atom that gives the sum of both protons and neutrons present in the nucleus.

• It is not the same as the atomic mass found on the periodic table.
• While the atomic number affects chemical properties, the mass number primarily influences isotopic characteristics.

Unlike the atomic number, the mass number changes only in certain types of decay:

• In alpha decay, it decreases by 4, since 2 protons and 2 neutrons are expelled.
• In beta-minus decay, it remains unchanged as there is a shift between neutrons and protons.

In our nuclear decay series, from \({}_{92}U^{238}\) to \({}_{91}Pa^{234}\), the mass number showcased these adjustments clearly. Recognizing the mass number helps understand isotopic stability and transformations in nuclear reactions.