Question

The element europium (EU) exists in nature as two isotopes: (151 EU)with a mass of 150.9196 amu & (153 EU) with a mass of 152.9209 amu. The average mass of EU is 151.96 How do you calculate the relative abundance of the two EU isotopes? X% times 150.9196 (plus) Y% times 152.9209 equals = 151.96. what are the X and Y percentages? And what is the formula to identify the unknowns X and Y?

Answer 1

X = 48.014%

Y = 51.986%

Step-by-step explanation:

Given

151 EU has a mass of 150.9196 amu

153 EU has a mass of 152.9209 amu

Calculating the relative abundance of the two EU isotopes.

First condition that must be satisfied is

X + Y = 100%;

X + Y = 1. ----- Equation 1

Second Condition is;

150.9196X + 152.9209Y = 151.96 ------ Equation 2

In Equation 1; make Y the subject of formula.

So, Y = 1 - X.

Substitute (1 - X) for Y in Equation 2

150.9196X + 152.9209(1 - X) = 151.96 ----Open bracket

150.9196X + 152.9209 - 152.9209X = 151.96 ---- Collect Like Terms

150.9196X - 152.9209X = 151.96 - 152.9209

−2.0013X = -0.9609

X = -0.9609/-2.0013

X = 0.480137910358267

X = 48.014% ----- Approximated

Y = 1 - X

Y = 1 - 48.014%

Y = 0.51986

Y = 51.986% ---- Approximated