# 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?

##### 1 Answer

#### 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

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

#"1 u " = " 1 proton " color(red)("OR") " 1 neutron"#

So, the average atomic mass of titanium will be

#m_"a" = "46 u" xx 0.08 + "47 u" xx 0.078 + "48 u" xx 0.734 + "49 u" xx 0.055 + "50 u" xx 0.053#

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