An element, X has the following isotopic composition `""^(56)X : 90% ""^(57)X : 8% ""^(57)X: 2.0%`. The weighted average atomic mass of the naturallyoccurring element X is closest to

Options

A. 56.14 amu
B. 56.8 amu
C. 60 amu
D. 55 amu

Answer

To calculate the weighted average atomic mass of the element X based on its isotopic composition, we can follow these steps:

### Step 1: Identify the isotopes and their percentages
The isotopes of element X and their respective percentages are:
- \(^{56}X\): 90%
- \(^{57}X\): 8%
- \(^{58}X\): 2%

### Step 2: Convert percentages to decimals
To use the percentages in calculations, we convert them to decimal form:
- \(^{56}X\): \(0.90\)
- \(^{57}X\): \(0.08\)
- \(^{58}X\): \(0.02\)

### Step 3: Multiply each isotope's mass by its percentage
Next, we multiply the mass of each isotope by its decimal percentage:
- For \(^{56}X\):
\[ 56 \times 0.90 = 50.4 \]
- For \(^{57}X\):
\[ 57 \times 0.08 = 4.56 \]
- For \(^{58}X\):
\[ 58 \times 0.02 = 1.16 \]

### Step 4: Sum the results
Now, we add the results from Step 3:
\[ 50.4 + 4.56 + 1.16 = 56.12 \]

### Step 5: Divide by the total percentage
Since the total percentage is 100%, we can directly use the sum calculated:
\[ \text{Average Atomic Mass} = 56.12 \, \text{AMU} \]

### Conclusion
The weighted average atomic mass of the naturally occurring element X is approximately \(56.12 \, \text{AMU}\).