Question

A nuclide undergoes two alpha decays, two positron decays, and two gamma decays. What is the difference between the atomic number of the parent nuclide and the atomic number of the daughter nuclide? A. 0 B. 2 C. 4 D. 6

Short answer

D. 6

Step-by-step solution

- Understand Alpha Decay

Each alpha decay reduces the atomic number by 2 because an alpha particle consists of 2 protons and 2 neutrons. So, after two alpha decays, the total reduction in the atomic number will be: \[ 2 \times 2 = 4 \]

- Understand Positron Decay

Each positron decay reduces the atomic number by 1 because a positron is a positively charged particle with the same mass as an electron. So, after two positron decays, the total reduction in the atomic number will be: \[ 2 \times 1 = 2 \]

- Understand Gamma Decay

Gamma decay does not change the atomic number because it involves the emission of a photon, which has no charge. Thus, the atomic number remains unchanged after gamma decay.

- Calculate the Total Change

Summing up the reductions from alpha and positron decays, the total difference in the atomic number is: \[ 4 + 2 = 6 \]

- Conclusion

Therefore, the difference between the atomic number of the parent nuclide and the atomic number of the daughter nuclide is 6.

Key concepts

alpha decay

Imagine an alpha particle, which consists of 2 protons and 2 neutrons bundled together. When a nuclide undergoes alpha decay, it ejects one of these alpha particles. Since protons determine the atomic number, losing 2 protons will decrease the atomic number by 2. Therefore, each alpha decay results in a loss of 2 in the atomic number. If a nuclide goes through two alpha decays, the reduction in the atomic number is: \[2 \times 2 = 4\] Alpha decay significantly alters the element because removing protons changes the identity of the element on the periodic table.
Alpha particles are relatively massive and carry a positive charge. They can be stopped by a piece of paper or the outer layer of human skin, but they are ionizing, which means they can damage living tissues if ingested or inhaled.

positron decay

Positron decay, or beta-plus decay, involves the emission of a positron from the nucleus of an atom. A positron is a particle with the same mass as an electron but with a positive charge. During positron decay, a proton in the nucleus is converted into a neutron, which emits a positron and a neutrino. The positron, being positively charged, will leave the atom. This conversion decreases the atomic number by 1 because there is now one less proton. Thus, each positron decay reduces the atomic number by 1. After two positron decays, the reduction is: \[2 \times 1 = 2\] Positron decay typically occurs in proton-rich nuclei. While a positron is not very penetrating, it will eventually annihilate on contact with an electron, releasing energy in the form of gamma rays.

gamma decay

Gamma decay differs from alpha and positron decay because it doesn't change the atomic number. Instead, gamma decay is the process of releasing excess energy from the nucleus. This energy is emitted in the form of gamma rays, which are high-energy photons. Since photons have no mass and no charge, they don't alter the number of protons or neutrons in the nucleus. Thus, gamma decay does not affect the atomic number. There is no numerical change to consider for gamma decay; its main effect is to bring the nucleus to a lower energy state. Gamma rays are highly penetrating and require dense materials like lead or thick concrete to be effectively blocked.

atomic number change

The atomic number is crucial because it defines what element an atom is. Changes in an atomic number can significantly alter the atom's identity and properties. In radioactive decay, different types of decay processes impact the atomic number differently:

• **Alpha Decay**: Decreases the atomic number by 2 for each decay event.
• **Positron Decay**: Decreases the atomic number by 1 for each decay event.
• **Gamma Decay**: Does not change the atomic number.

Given an example where a nuclide undergoes two alpha decays, two positron decays, and two gamma decays, we calculate the total change:

• Alpha decay totals: \[2 \times 2 = 4\]
• Positron decay totals: \[2 \times 1 = 2\]
• Gamma decay totals: \[0\]

Adding these changes together gives a total reduction of the atomic number by \[ 4 + 2 = 6\]. Therefore, the daughter nuclide will have an atomic number that is 6 less than the parent nuclide.