Question

The atomic mass of Gallium is 69.72 AMU. The masses of the naturally occurring isotopes are 68.9257 AMU and 70.908 AMU for Ga-69 and Ga-71. Find the percent (%) abundance for each.

Answer 1

40.7% abundance of Ga-71

59.93% abundance of Ga-69

Step-by-step explanation:

Given data:

Average atomic mass of Ga = 69.72 amu

Atomic mass of Ga-69 = 68.9257 amu

Atomic mass of Ga-71 = 70.908 amu

Percent abundance of each isotope = ?

Solution;

we know there are two naturally occurring isotopes of Ga.

First of all we will set the fraction for both isotopes

X for the isotopes having mass 68.9257

1-x for isotopes having mass 70.908

we will use the following equation,

68.9257x + 70.908 (1-x) = 69.72

68.9257x +70.908 - 70.908x = 69.72

68.9257x - 70.908x = 69.72 - 70.908

-1.9823x = - 1.188

x= 1.188/1.9823

x= 0.5993

0.5993 × 100 = 59.93 %

59.93 % is abundance of Ga-69 because we solve the fraction x.

now we will calculate the abundance of Ga-71.

(1-x)

1 - 0.5993 = 0.4007

0.4007× 100= 40.7 %

40.7 % for Ga-71.