Video Transcript
Magnesium exists as three isotopes: magnesium 24, magnesium 25, and magnesium 26. Their isotopic abundances are 79 percent, 10 percent, and 11 percent, respectively. What is the relative atomic mass of magnesium to one decimal place?
When we look at a cell on the periodic table, we often see a decimal value written at the bottom of the cell. This decimal value is the relative atomic mass. This mass is not the mass of an atom of boron but rather the average of the atomic masses of the isotopes of boron. Moreover, the relative atomic mass is not a straight average but a weighted average of the isotopic masses. The weighted average takes into account the abundance of each isotope. Abundance is the relative amount of each isotope and is frequently given as a percentage.
Relative atomic mass can be calculated by multiplying the isotope abundance times the isotope mass for each isotope of that element and adding the resulting values. To simplify the calculations, the mass number of an isotope is often used in place of the mass. The mass number is the sum of the number of protons and neutrons in the nucleus and is approximately equal to the exact mass of the atom in unified atomic mass units. In hyphen notation, the number after the hyphen is the mass number.
The question gives us the mass number and isotopic abundance for the three isotopes of magnesium. Before we substitute these values into the equation, we first need to convert the percentages into decimal notation. Percent means per 100. So to convert a percentage into decimal notation, we simply need to divide each percentage by 100. Thus, 79 percent become 0.79 in decimal notation, 10 percent is 0.1 in decimal notation, and 11 percent is 0.11 in decimal notation.
We can then substitute the isotopic abundance in decimal notation and the mass number into the equation for each isotope. We need to be careful to correctly match the mass number and percent abundance for each isotope. We perform the calculation and determine the relative atomic mass of magnesium to be 24.32. As isotopic abundance and mass number are unitless values, the relative atomic mass is also unitless. Finally, we should round our answer to one decimal place. With appropriate rounding, we have determined that the relative atomic mass of magnesium is 24.3.
