The element europium exists in nature as two isotopes: 151^Eu has a mass of 150.9196 amu, and 153^Eu has a mass of 152.9209 amu. The average atomic mass of europium is 151.96 amu. Calculate the relative abundance of the two europium isotopes.

I don't get it. :'( omg

x = fraction abundance 151 Eu

1-x = fraction abundance Eu153.

150.9196(x) + 152.9209(1-x) = 151.96.
Solve for x.
You may convert the fractions to percentages by multiplying each by 100.

Ahhhhh it's so confusing...

Uhm........

thank you Dr Bob!

It's good

To calculate the relative abundance of the two europium isotopes, we need to consider their masses and the average atomic mass of europium.

Let's assume that the relative abundance of the first isotope, 151Eu, is x, and the relative abundance of the second isotope, 153Eu, is 1-x.

We can use the following equation to calculate the average atomic mass:

Average atomic mass = (mass of isotope 1 * relative abundance of isotope 1) + (mass of isotope 2 * relative abundance of isotope 2)

To represent this equation:

151.96 amu = (150.9196 amu * x) + (152.9209 amu * (1-x))

Now we can solve this equation to find the value of x, which will give us the relative abundance of the first isotope, 151Eu.

151.96 amu = (150.9196 amu * x) + (152.9209 amu - 152.9209 amu * x)
151.96 amu = 150.9196 amu * x + 152.9209 amu - 152.9209 amu * x
151.96 amu - 152.9209 amu = 150.9196 amu * x - 152.9209 amu * x
-0.9609 amu = -2.0013 amu * x

Dividing both sides by -2.0013 amu:

x = -0.9609 amu / -2.0013 amu
x ≈ 0.4797

So the relative abundance of the first isotope, 151Eu, is approximately 0.4797 or 47.97%.

Since the relative abundance of the second isotope, 153Eu, is equal to (1-x), we can calculate it as follows:

Relative abundance of 153Eu = 1 - x
Relative abundance of 153Eu = 1 - 0.4797
Relative abundance of 153Eu = 0.5203 or 52.03%

Therefore, the relative abundance of 151Eu is approximately 47.97%, and the relative abundance of 153Eu is approximately 52.03%.