Question

Given that the abundances of isotopes ${}^{54}Fe,{}^{56}Fe$ and ${}^{57}Fe$ are 5%, 90% and 5% respectively, the atomic mass of Fe is:
A. 55.85
B. 55.95
C. 55.75
D. 56.05

Answer 1

Hint: Iron has naturally four isotopes with different percentages of abundance. We can calculate the atomic mass of iron using the following formula.
Average atomic mass of iron (Fe) = $\sum{{}}$ (abundance) (atomic mass of the isotope)

Complete answer:
- In the it is given that the abundances of isotopes ${}^{54}Fe,{}^{56}Fe$ and ${}^{57}Fe$ are 5%, 90% and 5% respectively.
- By using the given data we have to calculate the atomic mass of iron.
- Abundance of ${}^{54}Fe$ isotope = 5% and atomic mass is 54.
- Abundance of ${}^{56}Fe$ isotope = 90% and atomic mass is 56.
- Abundance of ${}^{57}Fe$ isotope = 5% and atomic mass is 57.
- There is a formula to calculate the atomic mass of an element by using the atomic mass of isotopes of the element and it is as follows.
Atomic mass = (abundance of 1st isotope $\times $ atomic mass of 1st isotope) + (abundance of 2nd isotope $\times $ atomic mass of 2nd isotope + (abundance of 3rd isotope $\times $ atomic mass of 3rd isotope) / 100
\[\begin{align}
  & \text{Atomic mass of the element=}\dfrac{(5\times 54)+(90\times 56)+(5\times 57)}{100} \\
 & \text{Atomic mass of the element}=\dfrac{270+5040+285}{100} \\
 & \text{Atomic mass of the element}=55.95amu \\
\end{align}\]
- Therefore the atomic mass of the iron is 55.95 amu.

So, the correct option is B.

Note:
We should know both the percentage of abundance of isotope and atomic mass of isotope to calculate the atomic mass of the element. Atomic mass of the element can be calculated by the average of the abundance of the isotope and their atomic masses.