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In a radioactive decay, an element \({z^X}^A\) emits four α- particles, three β- particles and eight gamma photons. The atomic number and mass number of the resulting final nucleus are 

In a radioactive decay, an element \({z^X}^A\) emits four α- particles, three β- particles and eight gamma photons. The atomic number and mass number of the resulting final nucleus are  Correct Answer Z – 5, A - 16

CONCEPT:

  • Radioactive decay: When n/p ratio of an atomic nucleus is high enough to make it unstable, it decays.
  • Radioactive decay mainly emits α- particles, β- particles and gamma rays.
  • What happens when an α- particle is emitted:
    • An alpha particle is identical to a helium nucleus, being made up of two protons and two neutrons bound together.
    • The original atom is changed into a different element.
    • Its mass number or atomic mass decreases by four and its atomic number by two.
    • Mass number A to A-4 and atomic number Z to Z-2.

ZXA —→ Z-2XA-4 + 2α4

  • What happens when a β- particle is emitted:
    • The electron leaves the atom as a beta particle but proton stays in the nucleus.
    • The original atom is changed into a different element.
    • The mass number or atomic mass stays the same but the atomic number increases by 1.
    • Mass number will remain same A and atomic number Z to Z+1. 

ZXA —→ Z+1XA + -1β0

  • What happens when γ- rays are emitted:
    • Gamma decay is the emission of energy in the form of photons from the nucleus of the atom.
    • Gamma rays are electromagnetic waves.
    • They are pure energy. They have no mass or atomic number.

CALCULATION:

  • Given that atomic number of element is X and mass number is A. There is emission four α- particles, three β- particles and eight gamma photons.
  • Emission of 1 α- particle will be equal to decrease in mass number by 4 and atomic number by 2.
  • Emission of 4 α- particle will be equal to decrease in mass number by 4 × 4 = 16 and atomic number by 4 × 2 = 8.
    • Mass number of element X will become A to A-16 and 
    • atomic number Z to Z-8.

ZXA —→ Z-8XA-16 + 4 2α4

  • Emission of 1 β- particle will be equal to increase atomic number by 1.
  • Emission of 3 β- particle will be equal to increase atomic number by 3.
    • Atomic number of element X will increase Z-8 to Z-5 and 
    • Mass number of element X will remain same A-16. 

Z-8XA-16 —→ Z-5XA-16 + 3 -1β0

  • Gamma decay will have no effect on mass or atomic number.
  • So Resultant element will have Mass number A-16 and atomic number Z-5. So the correct answer is option 3.

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