Question

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.

Answer 1

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

Answer 2

Answer:

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