Chlorine, consisting of two isotopes of mass numbers 35 and 37, has an atomic mass
Chlorine, consisting of two isotopes of mass numbers 35 and 37, has an atomic mass of 35.5. The relative abundance of the isotope of mass number 37 is _______
- A) 20
- B) 25
- C) 50
- D) 75
Correct Answer: B) 25
Explanation
Let's represent the relative abundance of the isotope with mass number 35 as x and the relative abundance of the isotope with mass number 37 as y. Since the sum of the relative abundances should be equal to 100%, we can write the equation:
x + y = 100
We know that the atomic mass of chlorine (35.5) is the weighted average of the isotopes. We can write this as:
(35 * x + 37 * y) / 100 = 35.5
Now we need to solve the system of equations to find the value of y, which is the relative abundance of the isotope of mass number 37.
x + y = 100
35x + 37y = 3550
Substitute x = 100 - y into the second equation:
35(100 - y) + 37y = 3550
3500 - 35y + 37y = 3550
2y = 50
Now divide by 2:
y = 25
Therefore, the relative abundance of the isotope of mass number 37 is 25 (Option B).