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

Answer 1

The correct option is A $\frac{A-Z-4}{Z-8}$

When a radio active subs undergoes

(i) $\alpha decay{K}_Z^A\to K_{Z-2}^{A-7}$

(ii) positron decay $K_Z^A\to K_{Z-2}^A$

$A\stackrel{3\alpha +2e^{+}}{\to }A-12$

$Z\stackrel{3\alpha +2e^{-}}{\to }Z-5$

$\frac{numofPnuetrons}{numofprotons}=\frac{A-Z-4}{Z-8}$