% Abundance

[s3a]

"The element europium exists in nature as two isotopes: Eu has a mass of 150.9196 u, and Eu has a mass of 152.9209 u. The average atomic mass of europium is 151.96 u. Calculate the relative abundance of the two europium."

Can someone help me do this?

Any help would be greatly appreciated!
Thanks in advance!

[Sonic]

"The element europium exists in nature as two isotopes: Eu has a mass of 150.9196 u, and Eu has a mass of 152.9209 u. The average atomic mass of europium is 151.96 u. Calculate the relative abundance of the two europium."

Can someone help me do this?

Any help would be greatly appreciated!
Thanks in advance!

Let the relative abundances be a and b respectively. Due to the nature of relative abundances it follows that a+b = 1 as these are the only two isotopes.

We can find out the fraction of each as a whole by multiplying the relative atomic mass of each isotope by it's fractional abundance. Mathematically:

Mr = aM1 + bM2

where Mr = average molecular mass, M1 = molecular mass of isotope a and M2 = molecular mass of isotope b

We know Mr, M1 and M2 so subbing them in:

151.96 = 150.9196a + 152.9209b .........(eq1)

Recalling our equation relating a and b and rearranging we get equation 2:

a = 1-b........(eq2)

eq1 and eq2 can now be solved simultaneously

[s3a]

Ok first of all, thanks for your reply,
I got lost with the a + b = 1 part and really do not understand what that's about.

As for your Mr = aM1 + bM2, here is my work (which you also illustrated above):

151.96u = (150.9196u)(a) + (152.9209u)(b)

I just cannot understand and prove to myself that a + b = 1. I am stuck at the equation above and confused with the fact that there are two variables.

To the best of my understanding, I think you are trying to form a system of equations (equating to equations) but I still am confused as to the specifics of what is going on.

[Sonic]

The question states that there are two, and only two, isotopes of this element. Therefore for any given amount of Eu must contain only the two isotopes - which I denoted as a and b before

The term Relative Abundance means the amount of each isotope as a fraction of the whole. As it's a fraction of the whole it follows that the sum of all the isotopes must equal 1 or 100% of the whole.

As there are only two isotopes of this element it follows that the sum of both must be 1. ie: a+b = 1

Is that better to understand?