Question

Question:Which nuclide(s) would you predict to be stable? Why?

(a)${}^{\mathbf{48}}\mathbf{}\mathbf{\text{K}}$

(b)${}^{\mathbf{79}}\mathbf{\text{Br}}$

(c)$\mathbf{argon}-\mathbf{32}$

Short answer

The stable nuclide is b)${}^{79}\text{Br}$.

Step-by-step solution

Definition of nuclide

Any species of atom that persists for a quantifiable period of time is referred to as a nuclide.

A: a large number

Z is the atomic number (number of protons)

N: the total number of neutrons (A - Z)

The neutron to proton ratio (isfor lighter nuclei.

The neutron to proton ratio increases as the mass of stable nuclei grows.

The ratio of N to Z in heavy nuclei is 1.5:1.

When and Z numbers are even, the nucleus is more stable than when S and Z numbers are odd.

Find if the nuclide in a) is stable

a)

${}^{48}K$
Atomic number of is nineteen
the number of protons is $Z=19$.

The number of neutrons is$Z=19$

Proton to nucleon quantitative relation is

$\begin{array}{rcl}Z& =& \frac{29}{19}\\ & =& 1.53:1\end{array}$

When we verify the graph, we will see that this nuclei has higher quantitative relation than zone of stability, thus it's unstable.

Find if the nuclide in b) is stable

b)

${}^{79}\text{Br}$

Atomic number ofis 35.
The number of protons is$Z=35$.

The number of neutrons is

$\begin{array}{rcl}N& =& A-Z\\ & =& 79-35\\ & =& 44.\end{array}$

Proton tonucleonquantitative relationis :

$\begin{array}{rcl}\frac{\text{N}}{\text{Z}}& =& \frac{44}{35}\\ & =& 1.26:1\end{array}$

This nuclei has thequantitative relationthat'sin zone of stability.

Thus, it's stable.

Find if the nuclide in c) is stable

c)

argon-32
Atomic number of Ar is eighteen.
The number of protons is Z = 32.

The number of neutrons is:

$\begin{array}{rcl}N& =& A-Z\\ & =& 32-18\\ & =& 14.\end{array}$

Proton tonucleonquantitative relationis:

$\begin{array}{rcl}\frac{\text{N}}{\text{Z}}& =& \frac{14}{18}\\ & =& 0.78:1\end{array}$

When wecross-checkthe graph,we willsee that this nuclei has lowerquantitative relationthan zone of stability.

Thus,it'sunstable.

The required graph is: