24.24 P - Chemistry: Molecular Nature Of Matter And Change

Question

Question: Why is ${}_{\mathbf{\text{24}}}{}^{\mathbf{\text{52}}}\mathbf{\text{Cr}}$ the most stable isotope of chromium?

Step-by-Step Solution

Answer

Because it has an even number of protons and neutrons, and the number of neutrons is a magic number (N=28).

Step 1: N/Z ratio

Neutron to proton ratio is important for lighter stable nuclei $\text{(N/Z)is} \text{1:1}$

As the mass of stable nuclei increases, neutron to proton ratio increases as well.

When the nucleus is more stable  . when the number is even   numbers are unusual.

Nuclides containing   the values of $\text{2,8,20,28,50,82(andN = 126)}$ are extremely stable. These are known as magic numbers and represent the number of protons and neutrons in filled nucleon levels. 

Step 2: Number of protons and Neutrons Cr 24 52

There are a total of protons Z=24.

The amount of neutrons is $\text{N = A - Z = 52 - 24 = 28}$

The proton-neutron ratio is  $\frac{\text{N}}{\text{Z}}\text{ = }\frac{\text{28}}{\text{24}}\text{ = 1.17:1}$

This isotope's stability is due to the fact that it's N/Z.

The ratio is stable because it has an even number of protons and neutrons, and the number of neutrons is a magic number N=28.

Step 3: Graphical representation of zone of stability

Let us plot the graph:

Therefore, the isotope's stability is due to the fact that it's N/Z. The ratio is stable.

Because it has an even number of protons and neutrons, and the number of neutrons is a magic number N=28.