A periodic table might list the average atomic mass of magnesium as being 24.312u, which the result of weighting the atomic masses of the magnesium isotopes is according to their natural abundances on Earth. The three isotopes and their masses are , , and . The natural abundance of is 78.99% by mass (that is, 78.99% of the mass of a naturally occurring sample of magnesium is due to the presence of).What is the abundance of (a) and (b) ?
The abundance of the three isotopes represents their percent of mass percent in the environment. Considering that there are three isotopes of magnesium, we can get an equation of the total abundance of the three isotopes to be 100% of the natural magnesium substance. Thus, using this concept, we can calculate the abundance of the two other isotopes that are unknown.
Let be the abundance of , let be the abundance of , and let be the abundance of . Then, the entry in the periodic table for Mg is:
Since, there are only three isotopes . Solving for and , we have the above equation as follows:
Now, substituting this above value and in equation (a), determine the abundance of isotope as follows:
Hence, the value of abundance is 9.303%.
Now, substitute the values and role="math" localid="1661585674376" in equation (b), solve to obtain the abundance of isotope as follows:
Hence, the value of abundance is 11.71%.
The radionuclide (T1/2 = 14.28 d) is often used as a tracer to follow the course of biochemical reactions involving phosphorus. (a) If the counting rate in a particular experimental setup is initially 3050 counts/s, how much time will the rate take to fall to 170 counts/s? (b) A solution containing is fed to the root system of an experimental tomato plant, and the activity in a leaf is measured 3.48 days later. By what factor must this reading be multiplied to correct for the decay that has occurred since the experiment began?
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