Question

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

• A. $\frac{A-Z-4}{Z-2}$
• B. $\frac{A-Z-8}{Z-4}$
• C. $\frac{A-Z-4}{Z-8}$
• D. $\frac{A-Z-12}{Z-4}$

Answer 1

Answer: (C)

When a radioactive nucleus emits an alpha particle, its mass number decreases by $4$ while the atomic number decreases by $2$.
When a radioactive nucleus, emits a $\beta^{+}$ particle (or positron $\left(e^{+}\right)$ ) its mass number remains unchanged while the atomic number decreases by $1$ .
$_{z}{X^{A}} \stackrel{3 \alpha}{\longrightarrow } _{z-6} Y^{A-12} \stackrel{2 e^{+}}{\longrightarrow } _{z-8} W^{A-12}$
In the final nucleus,
Number of protons, $N_{p}=Z-8$
Number of neutrons, $N_{n}=A-12-(Z-8)$
$=A-Z-4$
$\therefore \frac{N_{n}}{N_{p}}=\frac{A-Z-4}{Z-8}$