# Titanium has 5 isotopes: Ti-46 (8.0%), Ti-47 (7.8%), Ti-48 (73.4%), Ti-49 (5.5%), and Ti-50 (5.3%), what is the average atomic mass of titanium?

Oct 25, 2015

$\text{47.923 u}$

#### Explanation:

The idea here is that every isotope of titanium will have a contribution to the average atomic mass of the element proportional to its respective abundance.

Mathematically, the average atomic mass can be written as

color(blue)("avg. atomic mass" = sum_i ("isotope"_i xx "abundance"_i))

In your case, you know that you have a total of five isotopes, each with its specific percent abundance

• ""^46"Ti" -> 8.0% abundance
• ""^47"Ti" -> 7.8% abundance
• ""^48"Ti" -> 73.4% abundance
• ""^49"Ti" -> 5.5% abundance
• ""^50"Ti" -> 5.3% abundance

To calculate the average atomic mass, you can use the decimal abundance of the isotopes, which is simply the percent abundance divided by $100$.

The atomic mass of each isotope is given by its mass number, which indicates the number of protons and neutrons an isotope has in its nucleus.

These atomic masses are expressed in unified atomic mass units, or $u$, where

$\text{1 u " = " 1 proton " color(red)("OR") " 1 neutron}$

So, the average atomic mass of titanium will be

${m}_{\text{a" = "46 u" xx 0.08 + "47 u" xx 0.078 + "48 u" xx 0.734 + "49 u" xx 0.055 + "50 u}} \times 0.053$

m_"a" = color(green)("47.923 u")