Question

Which of the following is likely to be least stable?
(A) ${^{40}_{20}}Ca$
(B) ${^{55}_{25}}Mn$
(C) ${^{119}_{50}}Sn$
(D) ${^{30}_{13}}Al$

Answer 1

Heavier components are a lot of uncommon than lighter ones which implies that the light components are considerably more steady than weighty ones. There is an extraordinary transcendence of components of even nuclear number (Z) over components of odd, first brought up by Harkin, subsequently called Harkin's standard which has been affirmed by X-beam investigation, even on account of uncommon earths. This discovery implies that molecules of odd Z are significantly less steady than those of even Z.

Complete step by step answer
Magic number: The octet rule was figured from the perception that iotas with eight valence electrons were particularly stable (and normal). A comparative circumstance applies to cores with respect to the quantity of neutron and proton numbers that create stable (non-radioactive) isotopes. These "enchantment numbers" are common events in isotopes that are especially stable.
$n/P$ proportion is significant in the steadiness of radioactive substances.
In the event that $n$ and $p$ esteem is sorcery number i.e.,
$2,8,20,28,50,82,126$
at that point incredibly stable cores.
${^{40}_{20}}Ca$ $\Rightarrow$ $P{{ }} = {{ }}20$ (Magic Number)
${^{55}_{25}}Mn$ $\Rightarrow$ $P{{ }} = {{ }}25$ and $n{{ }} = {{ }}30$ (No enchantment Number)
${^{119}_{50}}Sn \Rightarrow$ $P{{ }} = {{ }}50$ (Sorcery Number)
${^{30}_{13}}Al$ $\Rightarrow$ $P{{ }} = {{ }}13$ and $n{{ }} = {{ }}17$ ( No wizardry Number)
On the off chance that ${N \mathord{\left/ {\vphantom {N P}} \right.} P}$ is proportion is equal(approx.) to 1 then radioactive substance is stable
Here ${^{55}_{25}}Mn$ $\Rightarrow$ ${N \mathord{\left/ {\vphantom {N P}} \right.} P}$ $= {{ }}30/25 = 1.2$
${^{30}_{13}}Al$ $\Rightarrow$ ${N \mathord{\left/ {\vphantom {N P}} \right.} P}$ $= 1.31.$ (Hence least stable)
So the answer is option D as it is less stable.

Additional Information
The principal factor for deciding if a core is stable is the neutron to proton proportion. Components with $\left( {Z < 20} \right)$ are lighter and these components' cores have a proportion of $1:1$ and want to have similar measure of protons and neutrons. Components that have nuclear numbers from 20 to 83 are weighty components, accordingly the proportion is extraordinary. The proportion is $1.5:1$ , the purpose behind this distinction is a result of the loathsome power between protons: the more grounded the repugnance power, the more neutrons are expected to balance out the cores.

Note
Out of the 280 isotopes that happen in nature, 154 are of even An and even Z, while there are just four with indeed, even An and odd Z. This implies that cores with even quantities of protons and neutrons are steadier than those with odd numbers. There are 107 stable isotopes cores having odd A, of which 55 have even Z and 52 having odd Z. Consequently, it follows that isotopes of even Z are substantially more plentiful also, consequently steadier than those of odd Z