Question

An element a exist in two isotopic forms a15 and a16. if the average atomic mass of a was found to be 15.24 then the % relative abundance of a15 will be

Answer 1

a15 means an isotope with relative atomic mass = 15


a16 means an isotope with relative atomic mass = 16


Let the percentage abundance of a15 = x%


The percentage abundance of a16 = 100 – x


The average atomic mass of a = [15x + 16(100-x)] / 100 = 15.24


15x + 16(100-x) = 1524


15x + 1600-16x = 1524


-x = -14576
x = 76


The percentage abundance of a15 = 76%

Answer 2

Answer: Percentage relative abundance of $A^{15}$ isotope is 76%

Explanation: We are given the average atomic mass of element A which is 15.24 amu.

Formula of average atomic mass:

$\text{Average Atomic Mass}=\sum_{i=1}^{n}(\text{Fractional abundance})_i\times (\text{Mass number})_i$

We take fractional abundance of $A^{15}$ isotope = x

Mass of $A^{15}$ isotope = 15 amu

Fractional abundance of $A^{16}$ isotope = (1 - x)

Mass of $A^{16}$ isotope = 16 amu

Putting all the values in the above equation, we get

$15.24=(15\times x)+(16\times (1-x))$

$x=0.76$

We are supposed to find the percentage abundance, so we multiply the fractional abundance by 100.

$\%\text{ abundance}=0.76\times 100$

Percentage abundance of $A^{15}$ = 76%