Given that the abundacne of isotopes `.^(54)Fe`, `.^(56)Fe`, and `.^(57)Fe` is 5%, 90% and 5% respectively. The atomic mass of `Fe` is

Options

A. 55.58
B. 55.95
C. 55.75
D. 55.05

Explanation

To calculate the atomic mass of iron (Fe) given the abundances of its isotopes, we can follow these steps:

### Step 1: Identify the isotopes and their abundances
We have three isotopes of iron:
- \( ^{54}Fe \) with an abundance of 5%
- \( ^{56}Fe \) with an abundance of 90%
- \( ^{57}Fe \) with an abundance of 5%

### Step 2: Write down the atomic masses of the isotopes
The atomic masses of the isotopes are:
- Atomic mass of \( ^{54}Fe \) = 54 u
- Atomic mass of \( ^{56}Fe \) = 56 u
- Atomic mass of \( ^{57}Fe \) = 57 u

### Step 3: Use the formula for average atomic mass
The average atomic mass can be calculated using the formula:
\[ \text{Average Atomic Mass} = \frac{\sum (\text{abundance} \times \text{atomic mass})}{\text{Total abundance}} \]

### Step 4: Calculate the contributions of each isotope
Now, we calculate the contribution of each isotope to the average atomic mass:
- Contribution of \( ^{54}Fe \):
\[ \text{Contribution} = 0.05 \times 54 = 2.7 \]
- Contribution of \( ^{56}Fe \):
\[ \text{Contribution} = 0.90 \times 56 = 50.4 \]
- Contribution of \( ^{57}Fe \):
\[ \text{Contribution} = 0.05 \times 57 = 2.85 \]

### Step 5: Sum the contributions
Now, we sum these contributions:
\[ \text{Total Contribution} = 2.7 + 50.4 + 2.85 = 55.95 \]

### Step 6: Calculate the average atomic mass
Since the total abundance is 100% (or 1 when expressed as a decimal), we can directly use the total contribution as the average atomic mass:
\[ \text{Average Atomic Mass} = 55.95 \text{ u} \]

### Final Answer
The atomic mass of iron (Fe) is approximately **55.95 u**.

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