Q. 4.114 - An Introduction to General, Organic, and Biological Chemistry

Question

There are four naturally occurring isotopes of Iron: ${}_{26}{}^{54}Fe, {}_{26}{}^{56}Fe, {}_{26}{}^{57}Fe and {}_{26}{}^{58}Fe$

a. How many protons, neutrons, and electrons are in ${}_{26}{}^{58}Fe$?

b. What is the most abundant isotope in an Iron sample?

c. How many neutrons are in ${}_{26}{}^{57}Fe$?

d. Why don't any of the isotopes of Iron have the atomic mass of $55.85 \mathrm{amu}$ listed on the periodic table?

Step-by-Step Solution

Answer

a. In ${}_{26}{}^{58}Fe$ the number of protons and electrons is $26$ and the number of neutrons is $32$.

b. The ${}_{26}{}^{56}Fe$ is the most abundant isotope.

c. The number of neutrons in ${}_{26}{}^{57}Fe$ is $31$.

d. The isotopes of Strontium with mass $55.85 \mathrm{amu}$ is not listed in the periodic table because of the weighted average.

Part (a) Step 1: Given Information

We need to find the number of protons, neutrons, and electrons in ${}_{26}{}^{58}Fe$.

Part (a) Step 2: Simplify

Using the basic representation of an atom, that is ${}_Z{}^{A}X$ in which $A$ is the mass number, $Z$ is the atomic number and $X$ is the atom.

For ${}_{26}{}^{58}Fe$, the number of protons and electrons is $26$

And neutrons is $A-Z$, i.e.

$$\begin{gathered} Neutrons=58-26 \\ Neutrons=32 \end{gathered}$$

Part (b) Step 1: Given Information

We need to find the abundant isotope in the Iron sample.

Part (b) Step 2: Explanation

To conclude the most prevalent Iron isotope. First, compare the isotopes to the weighted average in the periodic table. As the Iron has a weight average of $55.85 amu$, the most prevalent Iron isotope is ${}_{26}{}^{56}Fe$.

Part (c) Step 1: Given Information

We need to find the number of neutrons in ${}_{26}{}^{57}Fe$.

Part (c) Step 2: Calculation

Calculating the number of neutrons in ${}_{26}{}^{57}Fe$.

$$\begin{gathered} Neutrons=A-Z \\ Neutrons=57-26 \\ Neutrons=31 \end{gathered}$$

Part (d) Step 1: Given Information

We need to explain the reason for the isotopes of Iron with an atomic mass of $55.85 amu$ is not listed on the table.

Part (d) Step 2: Explanation

The isotopes of the Iron don't have an atomic mass of  $55.85 \mathrm{amu}$ due to the said value being the weighted average of the atomic masses of all of its existing isotopes.