Answer:
The abundance of the 13C isotope is 1.115%
Step-by-step 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%.