Question
A sample of magnesium is made up of 79% of magnesium -24 atoms, 10% of magnesium -25 atoms and 11% of magnesium -26 atoms. What is the relative atomic mass of magnesium?Calculate to 2 decimal places
Answer
4.2
(186 Votes)
Leonora
Master · Tutor for 5 years
Answer
1. To find {\displaystyle \delta ^{25}Mg} \delta ^{25}Mg, i.e., the amount of Mg-24, multiply the mass of the isotope (24 amu) by the proportion present (79%), giving us 24 x 0.79 = 18.962. To find {\displaystyle \delta ^{26}Mg} \delta ^{26}Mg, i.e., the amount of Mg-25, multiply the mass of the isotope (25 amu) by the proportion present (10%), giving us 25 x 0.10 = 2.52. To find {\displaystyle \delta ^{27}Mg} \delta ^{27}Mg, i.e., the amount of Mg-26, multiply the mass of the isotope (26 amu) by the proportion present (11%), giving us 26 x 0.11 = 2.86.4. Lastly, add up all the amounts to find the average relative atomic mass of the magnesium sample: 18.96 + 2.5 + 2.86 = 24.32 amu.
Explanation
The relative atomic mass of an element is not simply the mass of one atom, but the average mass of one atom, relative to the carbon-12 isotope (whose mass is defined as 12 exactly), taking into account the proportions of isotopes present. To digest the task at hand, the steps outlined below conform to how we can calculate the relative atomic mass:1. First, we look at isotopes and their abundances. Magnesium(Mg) has three naturally occurring isotopes: Mg-24, Mg-25 and Mg-26. As per the question: (a) Mg-24 has a thickness of 79%. (b) Mg-25 has a thickness of 10%. (c) Mg-26 has a thickness of 11%. 2. Quantify the contributions of each isotope to the overall relative atomic mass.Using the mass numbers as "relative atomic masses": (a) For Mg-24, contribution % = Mass number of isotope x abundance = 24 x 0.79; (b) For Mg-25, contribution % = Mass number of isotope x abundance = 25 x 0.10; (c) For Mg-26, contribution = Mass number of isotope x abundance = 26 x 0.11; We sum up all individual contributions by both the quantity of each isotope in the sample and their respective atomic masses to determine the overall relative atomic mass.Doing so allows us to get the average weight distinctive to magnesium as a composite of its isotope pool.