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Difficulty: MediumNatural Radioactivity and Radiation Emissions

A radioactive parent nucleus ZAX^{A}_{Z}\text{X} emits one α\alpha-particle and two β−\beta^--particles during a natural radioactive decay process to form a daughter nucleus Y\text{Y}. Which of the following correctly describes the relationship between the daughter nucleus Y\text{Y} and the parent nucleus X\text{X}?

  1. It is an isotope of the parent element with a mass number that is 4 units lower than that of the parent nucleus.Answer
  2. B
    It is an isobar of the parent element with an atomic number that is 2 units higher than that of the parent nucleus.
  3. C
    It is an isotope of the parent element with a mass number that is 2 units lower than that of the parent nucleus.
  4. D
    It is a different chemical element with an atomic number 2 units lower and a mass number 4 units lower.

Answer

The daughter nucleus is an isotope of the parent element with a mass number that is 4 units lower than that of the parent nucleus.
Emitting one alpha particle reduces the nucleus mass number by 4 and atomic number by 2. The subsequent emission of two beta-minus particles increases the atomic number by 2 (1 for each beta particle) without affecting the mass number. Consequently, the net change returns the atomic number to its original value ZZ, while the mass number is reduced by 4. Nuclei with identical atomic numbers belong to the same element and are classified as isotopes.

Step-by-Step Solution

1
Analyze the change in mass number (AA) and atomic number (ZZ) resulting from the emission of one α\alpha-particle (24He^{4}_{2}\text{He}).
The mass number becomes A−4A - 4 and the atomic number becomes Z−2Z - 2.
An alpha particle consists of 2 protons and 2 neutrons, so emitting it removes 4 units of mass and 2 units of atomic charge.
2
Analyze the change in mass number (AA) and atomic number (ZZ) resulting from the emission of two β−\beta^--particles (−10e^{0}_{-1}\text{e}).
The mass number remains (A−4)(A - 4) and the atomic number becomes (Z−2)+2=Z(Z - 2) + 2 = Z.
Each beta-minus particle is emitted when a neutron turns into a proton, increasing the atomic number by 1 while keeping the total mass number unchanged.
3
Compare the final nuclear numbers (A−4,Z)(A - 4, Z) of daughter nucleus Y\text{Y} with parent nucleus (A,Z)(A, Z).
Daughter Y\text{Y} has the same atomic number ZZ as parent X\text{X}, but its mass number is A−4A - 4.
Nuclides with the same atomic number ZZ but different mass numbers AA are isotopes of the same element.

Key Concept

Nuclear Decay Balancing and Isotopes
Estimated Time:1m 30s
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Topics

Natural Radioactivity and Radiation Emissions

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