An element X has the following isotopic composition:
`.^(200)X:90% .^(199)X:8.0% .^(202)X:2.0%`
The weight average atomic mass of the naturally occurring element X is closest to

Options

A. 201u
B. 202 u
C. 199 u
D. 200 u

Explanation

To find the weight average atomic mass of the element X given its isotopic composition, we can follow these steps:

### Step 1: Identify the isotopes and their abundances
The isotopes of element X and their respective abundances are:
- \( ^{200}X \): 90%
- \( ^{199}X \): 8%
- \( ^{202}X \): 2%

### Step 2: Convert percentages to fractions
To use these percentages in calculations, we convert them to fractions:
- \( ^{200}X \): \( \frac{90}{100} = 0.90 \)
- \( ^{199}X \): \( \frac{8}{100} = 0.08 \)
- \( ^{202}X \): \( \frac{2}{100} = 0.02 \)

### Step 3: Calculate the contribution of each isotope to the average atomic mass
Next, we multiply the atomic mass of each isotope by its fraction:
- Contribution from \( ^{200}X \): \( 200 \times 0.90 = 180 \)
- Contribution from \( ^{199}X \): \( 199 \times 0.08 = 15.92 \)
- Contribution from \( ^{202}X \): \( 202 \times 0.02 = 4.04 \)

### Step 4: Sum the contributions
Now, we sum the contributions from all isotopes:
\[ \text{Total contribution} = 180 + 15.92 + 4.04 = 199.96 \]

### Step 5: Calculate the average atomic mass
Since we have already summed the contributions, we can directly state that the average atomic mass is:
\[ \text{Average atomic mass} \approx 199.96 \]

### Step 6: Round the average atomic mass
Finally, we round the average atomic mass to the nearest whole number:
\[ \text{Rounded average atomic mass} \approx 200 \]

### Final Answer
The weight average atomic mass of the naturally occurring element X is closest to **200**.

---