Chapter 4.3, Problem 24SSC

Interpretation Introduction

Interpretation:

The atomic mass of magnesium needs to be determined, if three isotopes Mg-24, Mg-25 and Mg-26 have relative abundance of $79.99\%$, $10.00\%$ and $11.01\%$ respectively and have masses of $23.985amu$, $24.986amu$ and $\text{25}\text{.982 }amu$ respectively.

Concept introduction:  Isotope is the same number of protons and electrons but have a different number of neutrons in an atom of the same element. The atomic mass is the mass of all isotopes of the element that has been averaged together. The relative abundance is the percentage of atoms that have a specific atomic mass present in a naturally occurring element.

Answer to Problem 24SSC

The atomic mass of magnesium is $24.548amu$.

Explanation of Solution

Mass contribution of isotope Mg-24 is $(mass)\times (percentabundance)=23.985amu\times 0.7999amu=19.19amu$

Mass contribution of isotope Mg-25 is $(mass)\times (percentabundance)=24.986amu\times 0.1000amu=2.497amu$

Mass contribution of isotope Mg-26 is $(mass)\times (percentabundance)=25.982amu\times 0.1101amu=2.861amu$

Thus, the atomic mass of Magnesium (Mg) $=19.19amu+2.497amu+2.861amu=24.548amu$

Conclusion

Hence, $24.548amu$ is the atomic mass of magnesium.