Question

An unknown element is a mixture of isotopes ¹²⁰X and ¹²²X. The average atomic mass of X is 120.81 amu. What is the percent abundance of ¹²²X?

Answer 1

Answer:

40.5%  is abundance of X-122

Explanation:

we know there are two naturally occurring isotopes of X, X-120  and X-122.

First of all we will set the fraction for both isotopes

X for the isotopes having mass 122

1-x for isotopes having mass 12 0

The average atomic mass of X is 120.81 amu

we will use the following equation,

122x + 120 (1-x) = 120.81

122x + 120 - 120x = 120.81

122x- 120x = 120.81 -120

2x = 0.81

x= 0.81/2

x= 0.405

0.405 × 100 = 40.5%

40.5%  is abundance of X-122 because we solve the fraction x.

now we will calculate the abundance of X-120.

(1-x)

1 - 0.405 = 0.595

0.595  × 100 = 59.5 %

59.5 %  for X-120.