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Solution: Magnesium has three naturally occurring isotopes with the fo...

Question

Magnesium has three naturally occurring isotopes with the following masses and natural abundances:

Calculate the atomic mass of magnesium and sketch its mass spectrum. 

Video Transcript

Hey guys, in this question we're given the mass or atomic mass unit for each of the isotopes of magnesium as well as their abundances in percentage form, from this information we need to basically figure out what is the average mass of magnesium as well as figuring out the spectrum, so we're going to need to work this out guys so let's take a look here so this basically deals with the isotopes of magnesium so we're going to say that that their atomic mass which is really your average mass equals the mass of your isotope and since there is 3 of them this is mass of isotope 1 times its fractional abundance which you can abbreviate as just FA, now what's your fractional abundance? Your fractional abundance is just your percentage divided by a hundred and since is 3 isotopes that we're dealing with here so that would be the mass of isotope 2 times its fractional abundance which I'll abbreviate as Fa plus the mass of isotope 3 times its fractional abundance. Alright so we're going to plug this in so average mass or atomic mass equals so the mass of the first isotope is 23.9850, It's percentage is 78.99 percent which we're going to divide by a 100 to get its decimal form that represented its fractional abundance plus mass of the second isotope times its percentage divided by a hundred plus the mass of the third isotope Times its fractional abundance, OK? So, this equals 24.0305 AMU or atomic mass units so that's the atomic mass or average mass of magnesium. So, if you look on the periodic table you'll see that its mass on there is about that you might see 24.305 you might also see 24.31 depending on which type of periodic table you're looking at, now we need to sketch its spectrum, alright so this is its mass spectrum we're going to say up here represents its 100 percent intensity or absorbance, down here is its mass, alright so now how do we figure out their percentages? There's 3 isotopes, all we do here is we're going to take each one of their fractional abundances so this is the fractional abundance here of magnesium 24 and then we have magnesium 25 and then we have magnesium 26, OK? And each of them has a fractional abundance that's dividing their percentage by 100 and what we do here is we're going to say the one that has the largest fractional abundance we're going to divide all of them by that number then multiply it by 100, this will give us our intensity of each isotope in terms of the mass spectrum that we're drawing so this allowed 100 percent of absorbance or intensity, this will be 13 percent and this will be 14 percent so magnesium 24 weighs the least but it has the highest intensity 100 percent. Next, we have magnesium 25 it goes up to 13 percent and the magnesium 26 is a little bit higher because it's at 14 percent. Now this isn't drawn to scale this is just a rough drawing of it but that's the approach we take in order to draw the intensities or absorbance of each isotope in terms of the mass spectrum. The second part of this question not as commonly asked on exam but the first part for sure you need to remember the formula in how to calculate the average mass or the atomic mass.

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