# The relative atomic mass of rubidium is 85.56.Calculate the relative abundance of its 2 isotopes,Rb-85 and Rb-87

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The formula for relative atomic mass is simply:

Relative atomic mass = (total mass of atom)/(number of atoms)*Note: the 'number of atoms' is always assumed to be 100*

The specific formula is:

Relative Atomic Mass = [(Isotope **a** Mass x % abundance ) + (Isotope **b** Mass x % abundance)] / 100

Note that this formula does not limit the number of isotopes. If there are more isotopes, simply add more masses to the top of the equation.

This question can be solved using VERY simple algebra.

Here are the values of the equation laid out:` `

Relative Atomic Mass = 85.56

Pb-85 mass = 85

Pb-87 mass = 87

Let Pb-85 abundance = x

`:.` Pb-87 abundance = 1 - x

Subbing these values into the equation you get:

85.56 = 85x + 87(1 - x)

85.56 = 85x + 87 - 87x

-1.44 = 85x -87x

-1.44 = -2x

0.72 = x

0.72 `xx` 100 = 72%

`:.` The abundance of Pb-85 is 72%

100%-72% = 28%

` ` The abundance of Pb-87 is 28%

**Relative atomic mass** is defined as the average mass of an atom of a specific element as compared to the 12 carbon (C-12) isotope.

Relative atomic masses (RAM) can be calculated from isotopic data, using two things:

1) relative mass of each isotope

2) percentage abundance of each isotope

The **formula** is given below:

RAM = [(mass of isotope 1 x % abundance of isotope 1) + (mass of isotope 2 x % abundance of isotope 2)] / 100

Here,

RAM = 85.56

mass of isotope 1 = 85

mass of isotope 2 = 87

Let,

a1 = % abundance of isotope 1

a2 = % abundance of isotope 2

Therefore,

85.56 = [(85 x a1) + (87 x a2)] / 100

or (85 x a1) + (87 x a2) = 8556 .... (1)

Again, a1 + a2 = 100 (as they are % components)

or a1 = 100 - a2 .... (2)

Plugging in the value of a1 from equation (2) to equation (1), we get:

85 * (100 - a2) + 87 * a2 = 8556

or 8500 - 85 * a2 + 87 * a2 = 8556

or 2 * a2 = 56

or a2 = 56 / 2 = 28

Thus, % abundance of isotope 2 i.e. Rb-87 is **28%**

From equation (1):

a1 = 100 - a2 = 100 - 28 = 72

Thus, % abundance of isotope 1 i.e. Rb-85 is **72%**

The atomic mass of rubidium 85.56. It is made of two isotopes Rb-85 and Rb-87 that have atomic mass 85 and 87 respectively.

The atomic mass of rubidium is the weighted average of the mass of their isotopes. Let the percentage of Rb-85 be x, the percentage of Rb-87 is (1 - x).

The mass of rubidium is 85*x + 87*(1 - x) = 85.56

Solving the equation 85*x + 87*(1 - x) = 85.56 for x gives:

85x + 87 - 87x = 85.56

2x = 1.44

x = 72

Rubidium is made of 72% Rb-85 and 28% Rb-87