Question

rubidium has two isotope. 85 rb has mass of 84.9117 and 87 rb has a mass of 86.9085 amu. if the average atomic mass of rb is 85.4678 amu. what is the atomic abundance of each isotope?​

Answer 1

85Rb: 72.15%

87Rb: 27.85%

Step-by-step explanation:

The average atomic mass of an atom is the sum of all [atomic abundance of isotope]*[mass of isotope].

Rubidium has only two isotopes, so let the atomic abundance of 85Rb be x, thus making the atomic abundance of 87Rb equal to 1-x.

[Average atomic mass of Rb] = [Mass of 85Rb]*[atomic abundance of 85Rb] + [Mass of 87Rb]*[atomic abundance of 87Rb]

85.4678 = 84.9117x + 86.9085*(1-x)

85.4678 = 84.9117x + 86.9085 - 86.9085x

85.4678 = 84.9117x + 86.9085 - 86.9085x

-1.4407 = -1.9968x

Atomic abundance of 85Rb = x = 0.7215 = 72.15%

Atomic Abundance of 87Rb = 1 - x = 1 - 0.7215 = 0.2785 = 27.85%