# Gallium consists of 2 isotopes. One of those isotopes is 71-Ga with a mass of 70.92amu with an abundance of 39.892%. What is the mass number of the other isotope?

##### 1 Answer

#### Explanation:

At first glance, it may seem like the problem didn't provide you with enough information.

However, if you have access to a periodic table, you can determine the mass number of the second isotope by examining its atomic mass.

So, the key to this problem is the fact that gallium has **two isotopes**. This means that the *percent abundances* of these two isotopes **must** amount to

This means that the percent abundance of the second isotope will be equal to

#100% - 38.892% = 61.108%#

Now, pull up your periodic table and look for gallium,

Notice that gallium has an atomic mass of **weighted average** of the atomic masses of its naturally occurring isotopes.

#color(blue)("relative atomic mass" = sum_i ("isotope"_i xx "abundance"_i))#

This means that the **weighted average** of the atomic masses of its two isotopes **must** be equal to *decimal abundances*, which are simply percent abundances divided by

#"70.92 u" xx 0.38892 + color(blue)(x) xx 0.61108 = "69.72 u"#

Here

Solve this equation for

#color(blue)(n) = ("69.72 u" - "70.92 u" xx 0.38892)/0.61108 = "68.956 u"#

Now that you know the second isotope's atomic mass, you can find its mass number, which represents the number of protons **and** neutrons the isotope contains in its nucleus, by rounding this value **to the nearest whole number**.

In your case, the mass number of this second isotope will be

#68.956 -> color(green)(69)#