Magnesium has three naturally occurring isotopes: ²⁴Mg (23.985) with 78.99% abundance, ²⁵Mg (24.986) with 10.00% abundance, and a third with 11.01% abundance. Look up the atomic weight of magnesium, and then calculate the mass of the third isotope.

Video transcript

Hello, everyone. Today, we have the following problem. Element X has three naturally occurring isotopes with the following abundances. 68.89% abundance, we have 15% abundance and a third with 16.11 abundance. And the atomic wave of the element is 24.438 atomic mass units. Calculate the mass of the third isotope. So we can surmise that the atomic mass is equal to the mass, which is multiply by the abundance of isotope. One plus the mass multiplied by the abundance of the second isotope. And then we add the mass multiplied by the abundance of the third isotope. And so we know the atomic mass is 24.438 atomic mass units. And we equal that to the following. So we have our mass for the first one which is 23.966 am you, you multiply that by its abundance, which is 68 0.89%. But we divide that by 100 we get 0.6889 and we do the same for our second isotope. This time we have 24.965 atomic mass units multiplied by its abundance, which is 15% or 0.15. And then lastly, we have the mass of our third isotope. We multiply it by its abundance, which would be 0.16 11. Now, through rearranging this equation, we can get that the mass of our third isotope is equal to 24.438 atomic mass units. And then we subtract that by essentially everything that we have. So we have the mass and isotope abundance for our first one. And then we subtract by that of our second isotope. And this will all be divided by 0.16 11. In solving the math, we arrive at an answer of 25.966 atomic mass units as our answer or answer choice C and with that, we have solved the problem overall, I hope this helped. And until next time.