Carbon found nature as a mixture of C-12 and C-13. The average atomic mass of carbon is 12.011u. What is the percentage abundance of carbon-12 in nature ?

Answer

To find the percentage abundance of carbon-12 (C-12) in nature, we can use the formula for the average atomic mass of an element that has multiple isotopes. Here's a step-by-step solution:

### Step 1: Understand the Variables
We have two isotopes of carbon:
- C-12 with atomic mass \( M_1 = 12 \, u \)
- C-13 with atomic mass \( M_2 = 13 \, u \)

Let:
- \( A_1 = A \) (the fractional abundance of C-12)
- \( A_2 = 1 - A \) (the fractional abundance of C-13)

### Step 2: Write the Average Atomic Mass Equation
The average atomic mass \( M_{\text{average}} \) can be expressed as:
\[ M_{\text{average}} = (M_1 \cdot A_1) + (M_2 \cdot A_2) \]
Substituting the known values:
\[ 12.011 = (12 \cdot A) + (13 \cdot (1 - A)) \]

### Step 3: Expand and Rearrange the Equation
Expanding the equation gives:
\[ 12.011 = 12A + 13 - 13A \]
Combining like terms:
\[ 12.011 = 13 - A \]

### Step 4: Solve for A
Rearranging the equation to isolate \( A \):
\[ A = 13 - 12.011 \]
Calculating this gives:
\[ A = 0.989 \]

### Step 5: Calculate the Percentage Abundance
To find the percentage abundance of C-12:
\[ \text{Percentage of C-12} = A \times 100 = 0.989 \times 100 = 98.9\% \]

### Final Answer
The percentage abundance of carbon-12 in nature is **98.9%**.

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