Question

A radioactive nucleus (initial mass number $A_o$ 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. $\frac{A-Z-8}{Z-4}$
• B. $\frac{A-Z-4}{Z-8}$
• C. $\frac{A-Z-12}{Z-4}$
• D. $\frac{A-Z-4}{Z-2}$

Answer 1

Answer: (B)

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

Answer 2

In positive beta decay a proton is transformed into a neutron and a positron is emitted. $P^+ \longrightarrow n^0 + e^+$ no. of neutrons initially was A - Z no. of neutrons after decay (A - Z) - 3 x 2 (due to alpha particles) + 2 x 1 (due to positive beta decay) The no. of proton will reduce by 8. [as 3 x 2 (due to alpha particles) + 2(due to positive beta decay)] Hence atomic number reduces by 8.

The number of nuclei undergoing decay and the rate of decay per unit time are directly proportional to the total number of nuclei present in the given sample of the radioactive material, according to the law of radioactive decay, whenever the material experiences a decay.

Mathematical representation of the Law of radioactive decay:

The decay of the nucleus occurs in either of the 3 types of nuclear decay, namely:

1. Alpha (α) – decay: in this decay, the helium nucleus is emitted.
2. Beta (β) – decay: electrons are emitted.
3. Gamma (γ) – decay: In this decay, the high-energy photons are emitted.