# Naturally occurring europium (Eu) consists of two isotopes with a mass of 151 and 153. 151/63 Eu has an abundance of 48.03% and 153/63 Eu has an abundance of 51.97%. What is the atomic mass of europium?

Jun 23, 2014

The atomic mass of europium is 152 u.

Method 1

Assume that you have 10 000 atoms of Eu.

Then you have 4803 atoms of $\text{_63^151"Eu}$ and 5197 atoms of $\text{_63^153"Eu}$.

Mass of $\text{_63^151"Eu}$ = 4803 × 151 u = 725 253 u

Mass of $\text{_63^153"Eu}$ = 5197 × 153 u = 795 141 u

Mass of 10 000 atoms = 1 520 394 u

Average mass = $\frac{1520394 \text{u}}{10000}$ = 152 u

Method 2

$\text{_63^151"Eu}$: 48.03 % × 151 u = 72.5253 u

$\text{_63^153"Eu}$: 51.97 % × 153 u = 79.5141 u

Total = "152.0394 u" = 152 u

Note: In both methods, the answer can have only three significant figures, because that is all you gave for masses of the two isotopes.

Hope this helps.