Chlorine occurs in nature in two isotopic forms of masses 35 u and 37 u in the ratio of 3 : 1 respectively. What is the average atomic mass of the Chlorine atom?
- (a)36.1 u
- (b)35.5 u
- (c)36.5 u
- (d)35.1 u
Correct — B, 35.5 u. The average atomic mass is the weighted mean of the isotopic masses in their natural ratio. With Cl-35 and Cl-37 in the ratio 3 : 1, the average is (3 × 35 + 1 × 37) ÷ 4 = (105 + 37) ÷ 4 = 142 ÷ 4 = 35.5 u. This is why chlorine's atomic mass is listed as about 35.5 rather than a whole number.
- (a)36.1 u — This is not the 3 : 1 weighted mean; it would require a different abundance ratio than the one given.
- (c)36.5 u — 36.5 comes from weighting the isotopes wrongly; a simple 1 : 1 mix gives 36, while the 3 : 1 ratio gives 35.5.
- (d)35.1 u — This is below the correct weighted mean; the arithmetic 142 ÷ 4 gives 35.5, not 35.1.
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons, and so different masses. The average atomic mass of an element is the weighted mean of its isotopic masses, each weighted by its fractional abundance.
Weight each isotope by its share, three parts of 35 and one part of 37 over four total parts. The heavier isotope's smaller share pulls the average only slightly above 35, landing at 35.5.
- Average atomic mass equals the sum of each isotopic mass times its fractional abundance.
- For Cl-35 and Cl-37 in a 3 : 1 ratio, the average is (3×35 + 1×37) ÷ 4 = 35.5 u.
- This weighted mean explains why atomic masses are often non-integers.
- Isotopes share the same atomic number but differ in mass number.
Weighting Cl-35 and Cl-37 by the ratio 3 : 1 gives 35.5 u.
- Taking a simple average of 36 instead of the 3 : 1 weighted mean.
- Swapping the weights of the two isotopes.
Asked to compute an element's average atomic mass from isotope masses and their abundance ratio; use the weighted mean.
No directly related past PYQ was found.
- practice — not a real PYQ
Two isotopes of masses 10 u and 11 u occur in the ratio 1 : 4. The average atomic mass is
- (a)10.2 u
- (b)10.5 u
- (c)10.8 u
- (d)11.0 u
Answer(c) 10.8 u — (1×10 + 4×11) ÷ 5 = 54 ÷ 5.
- practice — not a real PYQ
Atomic masses of elements are often non-integers mainly because
- (a)electrons have mass
- (b)elements exist as a mixture of isotopes
- (c)protons vary in mass
- (d)of measurement error
Answer(b) elements exist as a mixture of isotopes.