Question

a mystery element has an average atomic mass of 25.16 amu. this mystery element has two naturally occuring isotopes. the first isotope has a relative abundance of 71.0% on and weighs 24 amu. what is the weight, in amu, of the second isotope?

Answer 1

28 AMU

Step-by-step explanation:

The average atomic mass consists of the relative masses of the isotopes, based on percent abundance.

Isotope Abundance(%) AMU Weighted AMU(Abundance*AMU)

1 71.0 24 17.04

2 29.0 x 0.29x [Spoiler: X = 28]

100.0 25.16 25.16

The goal is to find the weight, in amu, of isotope 2, such that when included with isotope 1 will result in an overall average of 25.16.

The table includes a "weighted AMU" column that is calculated by the product of the isotope AMU by it's percent abundance. [e.g., (24 AMU)(0.710) = 17.04AMU]

The sum of the weighted AMUs will equal the mystery element's average atomic mass. The AMU of isotope 2 is unknown, so we'll use "x" for the moment.

Now find the weighted average of these two isotopes. Write thisas an equation (units are AMU):

17.04 + 0.29x = 25.16

17.04 + 0.29x = 25.16

0.29x = 25.16 - 17.04

0.29x = 8.12

x = 28

Isotope Abundance(%) AMU Weighted AMU(Abundance*AMU)

1 71.0 24 17.04

2 29.0 28 8.12

100.0 25.16 25.16