Oxygen occurs in nature as a mixture of isotopes `""^16O, ""^17O " and " ""^18O` having masses of 15.995 u, 16.999 u and 17.999 u and relative abundance of 99.763%, 0.037% and 0.200% respectively. What is the average atomic mass of oxygen?

Options

A. 15.999 u
B. 16.999 u
C. 17.999 u
D. 18.999 u

Explanation

To find the average atomic mass of oxygen based on the given isotopes and their relative abundances, we will follow these steps:

### Step 1: Identify the isotopes and their properties
We have three isotopes of oxygen:
1. **Oxygen-16 (O-16)**:
- Mass = 15.995 u
- Relative abundance = 99.763%
2. **Oxygen-17 (O-17)**:
- Mass = 16.999 u
- Relative abundance = 0.037%
3. **Oxygen-18 (O-18)**:
- Mass = 17.999 u
- Relative abundance = 0.200%

### Step 2: Convert relative abundances from percentages to fractions
To use the formula for average atomic mass, we need to convert the percentages into fractions:
- A1 = 99.763% = 0.99763
- A2 = 0.037% = 0.00037
- A3 = 0.200% = 0.00200

### Step 3: Use the formula for average atomic mass
The average atomic mass (m_avg) is calculated using the formula:
\[ m_{avg} = \frac{\Sigma (m_i \cdot a_i)}{\Sigma a_i} \]
Where:
- \(m_i\) = mass of each isotope
- \(a_i\) = relative abundance of each isotope

### Step 4: Calculate the numerator
Calculate the contributions of each isotope to the average atomic mass:
\[ \text{Numerator} = (15.995 \, \text{u} \cdot 0.99763) + (16.999 \, \text{u} \cdot 0.00037) + (17.999 \, \text{u} \cdot 0.00200) \]
Calculating each term:
- For O-16: \(15.995 \times 0.99763 = 15.9524 \, \text{u}\)
- For O-17: \(16.999 \times 0.00037 = 0.00629 \, \text{u}\)
- For O-18: \(17.999 \times 0.00200 = 0.035998 \, \text{u}\)

Adding these together:
\[ \text{Numerator} = 15.9524 + 0.00629 + 0.035998 = 15.994688 \, \text{u} \]

### Step 5: Calculate the denominator
The denominator is the sum of the relative abundances:
\[ \text{Denominator} = 0.99763 + 0.00037 + 0.00200 = 1.00000 \]

### Step 6: Calculate the average atomic mass
Now, we can calculate the average atomic mass:
\[ m_{avg} = \frac{15.994688 \, \text{u}}{1.00000} = 15.994688 \, \text{u} \]

### Step 7: Round the result
Rounding to three decimal places, we find:
\[ m_{avg} \approx 15.995 \, \text{u} \]

### Final Answer:
The average atomic mass of oxygen is approximately **15.995 u**.

---