# What is the atomic mass of hafnium if, out of every 100 atoms, 5 have a mass of 176, 19 have a mass of 177, 27 have mass of 178, 14 have a mass of 179, and 35 have a mass of a 180?

Feb 13, 2016

$\text{Average atomic mass of Hafnium" =178.55" amu}$

#### Explanation:

If there are two isotopes an element

${\text{Average atomic mass" = "mass"_axx "fract"_a + "mass"_b xx "fract}}_{b}$
In the given problem about Hafnium, 5 isotopes have been given.
Extending the above expression to 5 isotopes
We obtain

$\text{Average atomic mass } = 176 \times 0.05 + 177 \times 0.19 +$
$178 \times 0.27 + 179 \times 0.14 + 180 \times 0.35$

$= 178.55$

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(Ensure that sum of all fractions adds to 1.

It is easy to find the fraction of each isotope in the question as total number is given as 100 atoms. Number of each isotope divided by 100)

Always use average atomic masses for mass calculations involving elements or compounds.