What is the atomic mass of hafnium if, out of every 100 atoms, 5 have a mass of 176amu, 19 have a mass of 177amu, 27 have a mass of 178amu, 14 have a mass of 179amu, and 35 have a mass of 180.0amu?

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?

Chemistry Atomic Mass

Average atomic mass of Hafnium

=

178.55

amu

Explanation:

If there are two isotopes an element

Average atomic mass

=

mass

a

×

fract

a

+

mass

b

×

fract

b

In the given problem about Hafnium, 5 isotopes have been given.

Extending the above expression to 5 isotopes

We obtain

Average atomic mass

=

176

×

0.05

+

177

×

0.19

+

178

×

0.27

+

179

×

0.14

+

180

×

0.35

=

178.55

-.-.-.-.-.-.-.-.-.-.-.-.-.-

(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.

a:

by the combination of an unlimited number of elements