24.19 P - Chemistry: Molecular Nature Of Matter And Change

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) $\mathbf{argon}-\mathbf{32}$

Step-by-Step Solution

Answer

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

Step 1: 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 (  is  for 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. 

Step 2: 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.

Step 3: Find if the nuclide in b) is stable

b) 

 ${}^{79}\text{Br}$

Atomic number of  is 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 to nucleon quantitative relation is :

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

This nuclei has the quantitative relation that's in zone of stability.

Thus, it's stable.

Step 4: 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 to nucleon quantitative relation is:

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

When we cross-check the graph, we will see that this nuclei has lower quantitative relation than zone of stability.

Thus, it's unstable.

The required graph is: