Naturally occurring magnesium is composed of two isotopes. Magnesium-24 has a mass of 23.9850 amu and
magnesium-26 has a mass of 25.9826 amu. The atomic mass of magnesium is 24.305 amu. What is the
percent abundance of each isotope?
Let x be the percent abundance of magnesium-24 and y be the percent abundance of magnesium-26.
The atomic mass of magnesium can be calculated using the formula:
atomic mass = (mass of isotope 1) * (percent abundance of isotope 1) + (mass of isotope 2) * (percent abundance of isotope 2)
Substituting the values given:
24.305 amu = 23.9850 amu * x + 25.9826 amu * y
We know that the percent abundances must add up to 100%, so:
x + y = 100
Simplifying the equation:
24.305 = 23.9850x + 25.9826y
x + y = 100
Solving this system of equations gives:
x = 0.778
y = 0.222
Therefore, the percent abundance of magnesium-24 is 77.8% and the percent abundance of magnesium-26 is 22.2%.