Question

A radioactive nucleus (initial mass number A and atomic number Z) emits 3 α- particles and 2 positrons. The ratio of the number of neutrons to that of protons in the final nucleus will be:

विकल्प

• ${\displaystyle \frac{\text{A}-\text{Z}-8}{\text{Z}-4}}$

• ${\displaystyle \frac{\text{A}-\text{Z}-4}{\text{Z}-8}}$

• ${\displaystyle \frac{\text{A}-\text{Z}-12}{\text{Z}-4}}$

• ${\displaystyle \frac{\text{A}-\text{Z}-4}{\text{Z}-2}}$

Answer 1

${\displaystyle \frac{\text{A}-\text{Z}-4}{\text{Z}-8}}$

Explanation:

The mass number reduces by 4 units and the atomic number decreases by 2 units as a result of 1 α-particle emission. The atomic number reduces by one unit with each positron emitted, but the mass number remains constant.

∴ Mass number of final nucleus = A − 12

Atomic number of final nucleus = Z − 8

∴ Number of neutrons = (A − 12) − (Z − 8)

=A − Z − 4

Number of protons = Z − 8

∴ Required ratio = ${\displaystyle \frac{\text{A}-\text{Z}-4}{\text{Z}-8}}$