The atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes. The weighting factor for each isotope is its fractional abundance.

Step 1: Understand the formula for Average Atomic Mass

The average atomic mass is calculated using the following formula: $\text{Average Atomic Mass} = \sum (\text{Isotopic Mass} \times \text{Fractional Abundance})$ We can approximate the isotopic mass with the given mass number for each isotope.

Step 2: List the given data

We are given the following information for the isotopes of Iron (Fe):

• Isotope 1: $^{54}$Fe
  • Mass Number $\approx$ Isotopic Mass = 54 u
  • Abundance = 5%
• Isotope 2: $^{56}$Fe
  • Mass Number $\approx$ Isotopic Mass = 56 u
  • Abundance = 90%
• Isotope 3: $^{57}$Fe
  • Mass Number $\approx$ Isotopic Mass = 57 u
  • Abundance = 5%

Step 3: Convert percentage abundances to fractional abundances

To use the formula, we need to convert the percentage abundances into fractional (decimal) form by dividing by 100.

• Fractional abundance of $^{54}$Fe = $5 / 100 = 0.05$
• Fractional abundance of $^{56}$Fe = $90 / 100 = 0.90$
• Fractional abundance of $^{57}$Fe = $5 / 100 = 0.05$

(Check: The sum of fractional abundances is $0.05 + 0.90 + 0.05 = 1.00$, as expected.)

Step 4: Calculate the average atomic mass of Fe

Now, we plug the values into the formula:

$\text{Atomic Mass of Fe} = (\text{Mass of } ^{54}\text{Fe} \times \text{Abundance of } ^{54}\text{Fe}) + (\text{Mass of } ^{56}\text{Fe} \times \text{Abundance of } ^{56}\text{Fe}) + (\text{Mass of } ^{57}\text{Fe} \times \text{Abundance of } ^{57}\text{Fe})$

$\text{Atomic Mass of Fe} = (54 \times 0.05) + (56 \times 0.90) + (57 \times 0.05)$

Calculate each term:

• $54 \times 0.05 = 2.70$
• $56 \times 0.90 = 50.40$
• $57 \times 0.05 = 2.85$

Sum the terms to find the average atomic mass:

$\text{Atomic Mass of Fe} = 2.70 + 50.40 + 2.85 = 55.95 \text{ u}$

Step 5: Compare the result with the given options

The calculated atomic mass is 55.95.

• A: 55.85
• B: 55.95
• C: 55.75
• D: 56.05

The calculated value matches option B.