naturally occurring europium (eu) consists of two isotopes was a mass of 151 and 153. europium- 151 has an abundance of 48.03% and europium -153 has an abundance of 51.97%. what is the atomic mass of europium?

Answer 1

To calculate the atomic mass of europium based on its isotopes, we use the formula for the weighted average of the masses of the isotopes based on their relative abundances.

The formula is given by:

\[ \text{Atomic Mass} = ( \text{mass of } ^{151}\text{Eu} \times \text{abundance of } ^{151}\text{Eu} ) + ( \text{mass of } ^{153}\text{Eu} \times \text{abundance of } ^{153}\text{Eu} ) \]

Given:

• Mass of \( ^{151}\text{Eu} = 151 , \text{amu} \)
• Mass of \( ^{153}\text{Eu} = 153 , \text{amu} \)
• Abundance of \( ^{151}\text{Eu} = 48.03% = 0.4803 \)
• Abundance of \( ^{153}\text{Eu} = 51.97% = 0.5197 \)

Now we can substitute these values into the formula:

\[ \text{Atomic Mass} = (151 \times 0.4803) + (153 \times 0.5197) \]

Calculating each term:

1. \( 151 \times 0.4803 = 72.4893 \)
2. \( 153 \times 0.5197 = 79.5771 \)

Now add the two results together:

\[ \text{Atomic Mass} = 72.4893 + 79.5771 = 152.0664 , \text{amu} \]

Therefore, the atomic mass of europium is approximately 152.07 amu (rounded to two decimal places).