Question

An unknown element X has the following isotopes: 52^ X (90.00% abundant, 49^X (8.00% abundant), 50^X (2.00% abundant). What is the approximate atomic mass of X?

Answer 1

Answer: The average atomic mass of X is 51.72 amu.

Explanation:

Average atomic mass of an element is defined as the sum of masses of each isotope each multiplied by their natural fractional abundance.

Formula used to calculate average atomic mass follows:

$\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i$   .....(1)

• For $^{52}\textrm{X}$ isotope:

Mass of $^{52}\textrm{X}$ isotope = 52 amu

Percentage abundance of $^{52}\textrm{X}$ isotope = 90.00 %

Fractional abundance of $^{52}\textrm{X}$ isotope = 0.9000

• For $^{49}\textrm{X}$ isotope:

Mass of $^{49}\textrm{X}$ isotope = 49.00 amu

Percentage abundance of $^{49}\textrm{X}$ isotope = 8.00 %

Fractional abundance of $^{49}\textrm{X}$ isotope = 0.0800

• For $^{50}\textrm{X}$ isotope:

Mass of $^{50}\textrm{X}$ isotope = 50.00 amu

Percentage abundance of $^{50}\textrm{X}$ isotope = 2.00 %

Fractional abundance of $^{50}\textrm{X}$ isotope = 0.0200

Putting values in equation 1, we get:

$\text{Average atomic mass of X}=[(52\times 0.90)+(49\times 0.08)+(50\times 0.02)]\\\\\text{Average atomic mass of X}=51.72amu$

Hence, the average atomic mass of X is 51.72 amu.