Question

question 6 of 30
the average atomic mass of carbon is 12.01 amu. based on the atomic masses of the two isotopes of carbon, how do the relative abundances of the isotopes compare?

isotope	atomic mass (amu)
c - 13	13.003

a. they are about the same.
b. there is a very small percentage of c - 12.
c. there is a slightly larger percentage of c - 12 than c - 13.
d. there is a very large percentage of c - 12.

Explanation:

Step1: Set up the average - atomic - mass formula

Let the relative abundance of C - 12 be $x$ (where $x$ is a decimal between 0 and 1), then the relative abundance of C - 13 is $1 - x$. The average atomic mass formula is $Average\ atomic\ mass=(Atomic\ mass\ of\ C - 12\times x)+(Atomic\ mass\ of\ C - 13\times(1 - x))$.

Step2: Substitute the given values

We know that the average atomic mass of carbon is 12.01 amu, the atomic mass of C - 12 is 12.000 amu, and the atomic mass of C - 13 is 13.003 amu. So, $12.01 = 12.000x+13.003(1 - x)$.

Step3: Expand and solve for $x$

Expand the right - hand side: $12.01=12.000x + 13.003-13.003x$. Combine like terms: $12.01-13.003=(12.000x-13.003x)$. So, $- 0.993=-1.003x$. Then $x=\frac{13.003 - 12.01}{13.003 - 12.000}=\frac{0.993}{1.003}\approx0.99$.

Answer:

D. There is a very large percentage of C - 12.