Question

In the reaction represented by \({ }_{\mathrm{Z}} \mathrm{X}^{\mathrm{A}} \longrightarrow \mathrm{z}_{\mathrm{z}-2} \mathrm{Y}^{\mathrm{A}-4} \longrightarrow{\mathrm{z}-2} \mathrm{Y}^{\mathrm{A}-4} \longrightarrow{\mathrm{z}-1} \mathrm{~K}^{\mathrm{A}-4}\) The decays in the sequence are (a) \(\alpha, \beta, \gamma\) (b) \(\beta, \gamma, \alpha\) (c) \(\gamma, \alpha, \beta\) (d) \(\alpha, \gamma, \beta\)

Short answer

The sequence of decays is \(\alpha, \gamma, \beta\), which corresponds to option (d).

Step-by-step solution

Understand the Reaction Sequence

The sequence provided is for a nuclear reaction involving a series of decays, represented by \( { }_{\mathrm{Z}} \mathrm{X}^{\mathrm{A}} \longrightarrow\mathrm{z}_{\mathrm{z}-2} \mathrm{Y}^{\mathrm{A}-4} \longrightarrow{\mathrm{z}-2} \mathrm{Y}^{\mathrm{A}-4} \longrightarrow{\mathrm{z}-1} \mathrm{~K}^{\mathrm{A}-4} \). To understand this, we'll analyze each transition and determine which type of decay fits the changes.

Analyze First Transition

The first transition is from \( { }_{\mathrm{Z}} \mathrm{X}^{\mathrm{A}} \rightarrow \mathrm{z}_{\mathrm{z}-2} \mathrm{Y}^{\mathrm{A}-4} \). This suggests a decrease of 2 in the atomic number and 4 in the mass number. This is typical of an alpha decay, where an alpha particle (\(^{4}_{2}\mathrm{He}\)) is emitted.

Analyze Second Transition

The next transition is from \( \mathrm{z}_{\mathrm{z}-2} \mathrm{Y}^{\mathrm{A}-4} \rightarrow {\mathrm{z}-2} \mathrm{Y}^{\mathrm{A}-4} \). Here, there is no change in the atomic number or the mass number. This is characteristic of a gamma decay, where energy is released but no change occurs in the A or Z.

Analyze Third Transition

The final transition is from \( {\mathrm{z}-2} \mathrm{Y}^{\mathrm{A}-4} \rightarrow {\mathrm{z}-1} \mathrm{~K}^{\mathrm{A}-4} \). Here, there is an increase in the atomic number by 1, but the mass number remains the same. This indicates a beta decay, where a neutron is converted into a proton, emitting a beta particle.

Key concepts

Alpha Decay

Alpha decay is a type of nuclear decay where an unstable atom emits an alpha particle to become more stable. An alpha particle is composed of two protons and two neutrons, which is essentially a helium nucleus, represented as \({}^{4}_{2}\mathrm{He}\). During alpha decay, the parent nucleus loses two protons and two neutrons.
This results in the atomic number decreasing by 2, and the mass number decreasing by 4.

Alpha decay is common in heavy elements like uranium or radium.

• This reduction stabilizes the atom more compared to its previous state.
• Therefore, we can identify alpha decay by detecting the typical changes in the nucleus: a loss of 4 in mass number and a loss of 2 in atomic number.

Gamma Decay

Gamma decay occurs when an excited nucleus releases excess energy in the form of gamma radiation, which is high-energy electromagnetic radiation.
This process doesn't alter the number of protons or neutrons in the nucleus, meaning both the mass number (A) and the atomic number (Z) stay unchanged after gamma decay.

Gamma rays are incredibly penetrating and need dense materials like lead to be effectively blocked.

• Gamma decay often follows other types of decay like alpha or beta decay, as the nucleus remains in an excited state and needs to shed energy to reach its ground state.
• Despite not changing the nucleus's composition, gamma decay contributes significantly to the radiation's penetrating power.

Therefore, it’s crucial to recognize that gamma decay involves the emission of energy without altering the nuclei's other properties.

Beta Decay

Beta decay is another form of nuclear decay, where a neutron is converted into a proton within the nucleus, and a beta particle is emitted. A beta particle is essentially an electron (or positron) that is emitted from the nucleus.
During this process, the atomic number of the element increases by one, since a neutron converts to a proton, but the mass number remains the same because the overall count of nucleons is unchanged.

Beta decay comes in two types: beta-minus (negative) decay and beta-plus (positive) decay.

• In beta-minus decay, an electron and an antineutrino are emitted, which causes the increase in atomic number.
• In beta-plus decay, a positron and a neutrino are emitted, generally decreasing the atomic number.

This decay mode illustrates the transformation of subatomic particles, showcasing the delicate balance of forces in the atomic nucleus.