Naturally occuring element Z consists of Z-24 (mass=23.99), Z-25 (mass=24.99), and Z-26 (mass=25.98). If the natural abundance of Z-25 is 10.0% and the isotope ratio Z-24/Z-26 is 7.174, what is the natural abundance of the lightest isotope?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Since Z-25 makes up 10% of the element Z in nature the remaining 90% must be the sum of other two isotopes, Z-24 and Z-26. We know that the percent abundance of X-24 is 7.174 times that of Z-26, so we can find the abundance of both isotopes as follows:

Let Z-24 = x and Z-26 = 0.90-X 

x/(0.90-x) = 7.174

x = (7.174)(0.90-x)

8.174x = 6.454

x = 0.7897

Z-24 is the lightest isotope:

abundance of Z-24 = 0.7897 = 78.97%

The abundance of Z-26 is 0.1103 = 11.03%

The given masses of the isotopes aren't needed to solve this problem. However, you could use them to find the average mass of element Z in nature since you now know the relative amounts of each isotope. The average mass is the sum of the mass of each isotope multiplied by its percent abundance. 

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team