Question

Gallium has two naturally occurring isotopes. One of them, gallium-69, has a mass of 68.925581 u and a percent isotopic abundance of 60.11%. What must be the mass and percent isotopic abundance of the other isotope, gallium-71?

Answer 1

1) The percent isotopic abundance of Ga-71 = 39.89%.

2) The mass of Ga-71 = 70.294625 u.

Step-by-step explanation:

1) The percent isotopic abundance of Ga-71:

The total sum of different isotopes = 100%.

∴ The abundance percent of Ga-69 + the abundance percent of Ga-71 = 100%.

∴ The abundance percent of Ga-71 = 100% - The abundance percent of Ga-69 = 100% - 60. 11% = 39.89%.

2) The mass of Ga-71:

∵ The amu of the mixture = (amu of Ga-69)(fraction of isotope Ga-69) + (amu of Ga-71)(fraction of isotope Ga-71).

The amu of the mixture = 69.723 u,

amu of Ga-69 = 68.925581 u, fraction of isotope Ga-69 = (abundance of Ga-69)/100 = (60.11%)/100 = 0.6011,

amu of Ga-71 = ??? u, fraction of isotope Ga-71= (abundance of Ga-69)/100 = (39.89%)/100 = 0.3989.

∴ 69.723 u = (68.925581 u)(0.6011) + (amu of Ga-71)(0.3989).

∴ (amu of Ga-71)(0.3989) = (69.723 u)(68.925581 u)(0.6011) = 28.29 u.

∴ (amu of Ga-71) = (28.29 u)/(0.3989) = 70.294625 u.