The common isotopes of carbon are 12C and 13C. The average mass of carbon is 12.01115 amu. What is the abundance of the 13C isotope? A. 1.115% B. 98.885% C. 0.480% D. 99.52% Provide an explanation if possible. Thanks so much!

The abundance of the 13C isotope is 1.115%

Explanation:

The given information are;

Common isotope of carbon are 12C and 13C

The formula for calculating the relative atomic mass is the observed mass multiplied by the percentage abundance at that mass given as follows;

M₁ X₁ + M₂X₂ = Relative atomic mass

Where:

X₁ + X₂ = 1 as these are percentage represented as fractions

Let M₁ = 12 for 12C and M₂ = 13 for 13C

X₁ = Relative abundance fraction of 12C

X₂ = Relative abundance fraction of 13C

We have;

12X₁ + 13X₂ = 12.01115(1)

X₁ + X₂ = 1(2)

Which gives;

X₁  = 1 - X₂

Substituting the value for X₁ in equation (1) gives;

12(1 - X₂) + 13X₂ = 12.01115

13X₂ - 12X₂ + 12 = 12.01115

X₂ = 12.01115 - 12 = 0.01115

Therefore, the relative abundance fraction of 13C 0.01115 which in percentage is 100 × 0.01115  = 1.115%.