Question

A plot of the number of neutrons ($n$) against the number of protons ($p$) of stable nuclei exhibits upward deviation from linearity for atomic number, $Z>20$. For an unstable nucleus having $n/p$ ratio less than $1$, the possible mode(s) of decay is (are)

• A. ${\beta }^{-}-\text{decay}(\beta -\text{emission})$
• B. Orbital or K-electron capture
• C. Neutron emission
• D. ${\beta }^{+}$ - decay (positron emission)

Answer 1

Answer: (B), (D)

${\beta }^{+}$ - decay (positron emission)

All the nuclei tends to maintain its $\frac{n}{p}$ ratio around 1-1.5 range. So if any nuclei have $\frac{n}{p}$ ratio less than 1 then it wants to increase it either by gaining neutron or lossing proton.

a) $\beta decay$
$A\to X+{}_{-1}^{0}e$
In this decay there is an increament in $p$ which furthur decreases the ratio.

b) $OrbitalorK-electroncapture$
$A+{}_{-1}^{0}e\to X$
In this process there is a decreament in $p$ which increases the ratio and stability.

c) $Neutronemission$
$A\to X+{}_0^{1}n$
Here, there is loss of $n$ which decreases the ratio and stability.

d) $Positronemission$
$A\to X+{}_{+1}^{0}e$
In this process there is a decreament in $p$ which increases the ratio and stability.