Question

Chlorine has two isotopes $^{35}Cl$ and $^{37}Cl$ with average atomic mass of 35.5. What is the ratio of their relative abundance respectively?

• A. 1 : 1
• B. 2 : 1
• C. 1 : 3
• D. 3 : 1

Answer 1

Answer: (D)

3 : 1

Answer 2

Let the relative abundances of $^{35}Cl$ and $^{37}Cl$ be $a$ and $b$ respectively, with

$$a + b = 1.$$

The average atomic mass is given by:

$$35a + 37b = 35.5.$$

Substitute $a = 1 - b$ into the equation:

$$35(1 - b) + 37b = 35.5 \\ 35 - 35b + 37b = 35.5 \\ 35 + 2b = 35.5 \\ 2b = 0.5 \\ b = 0.25 \quad\text{and}\quad a = 0.75.$$

Thus, the ratio of the relative abundance (in the order $^{35}Cl : \, ^{37}Cl$) is:

$$0.75 : 0.25 = 3 : 1.$$