The element europium exists in nature as two isotopes: 151eu has a mass of 150.9196 amu, and 153eu 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.

Two isotopes of europium are 151eu and 153eu

Mass of 151eu = 150.9196 amu

Mass of 153eu = 152.9209 amu

Average atomic mass = 151.96 amu

Let x and y are the relative abundance of two isotopes of europium are 151eu and 153eu

So, x% times 150.9196 + y% times 152.9209 = 151.96

x150.9196 + y152.9209 = 151.96

And x + y = 100% = 1, from here x = 1 - y and y = 1 - x

Solve these equation by substitution,

By replacing x = 1-y, we get

(1-y) 150.9196 + y152.9209 = 151.96

150.9196 - 150.9196y + y152.9209 = 151.96

2.0013y = 1.0404

Y = 0.5199 = 51.99%

Using the value of y we get,

X = 1-y = 1-51.99 = 0.4801 = 48.01%

So, relative abundance of two isotopes of europium are 151eu and 153eu are 48.01% and 51.99% respectively