Question

Chlorine has two stable isotopes Cl-35 and Cl-37 with atomic masses 34.96 and 36.95 respectively. If the avg mass of chlorine is 35.43. Calculate the percentage of abundance.

Answer 1

Hint: Isotopes are the elements that have the same number of protons and have different numbers of neutrons. Means isotopes have the same atomic number and different mass number. The percentage of abundance of isotopes is going to depend on the stability of the element.

Complete answer:
- In the question it is given that chlorine has two isotopes Cl-35 and Cl-37 with atomic masses 34.96 and 36.95.
- We have to calculate the percentage of abundance of the isotopes of the chlorine from the given data.
- We know that the total percentage of the abundance of chlorine isotopes is 100.
- Assume that Cl-34.96 is x and Cl-36.95 is 100-x.
- In the question it is given that the average mass of chlorine is 35.43 means the average mass of the isotopes is 35.43.
- Therefore
\[\begin{align}
  & 35.43=\dfrac{(34.96\times x)+(36.95\times (100-x))}{100} \\
 & 3545=34.96x+3695-36.95x \\
 & 36.95x-34.96x=3695-3545 \\
 & 1.98x=150 \\
 & x=75.75\text{ % }\!\!\!\!\text{ } \\
\end{align}\]
- We know that Cl-34.96 is x.
- Means the percentage of abundance of Cl-34.96 is 75.75 %.
- Coming to Cl-36.95 is 100-x.
- Substitute the value of x in the 100-x to get the percentage of abundance of Cl-36.95.
- Therefore the percentage of abundance of Cl-36.95 = 100 – 75.75 = 24.25 %.
So, the percentage of abundance of cl-34.96 and 36.95 are 75.75 % and 24.25% respectively.

Note:
The percentage of abundance of the isotopes is going to depend on the stability of the isotopes. Chlorine 34.96 is more stable than Cl-36.95. That is why the percentage of abundance of Cl-34.96 is high when compared to Cl-36.95.