The atomic mass of fictitious element X is 51.70 amu. If element X consists of two isotopes that have mass numbers of 50 and 52, what is the approximate % natural abundance of each isotope?

1 Answer
Oct 20, 2016

% abundance of isotope with mass 50: 15%

% abundance of isotope with mass 52: 85%

Explanation:

Write the equation for relative atomic mass in terms of x (with x being one isotope's mass) and solve for x:

51.70 = ((x*50)+((100-x)*52))/100

5170 = (x*50)+((100-x)*52))

5170 = 50x+5200-52x

5170 = 5200-2x

-30=-2x

x=15

Find the value of y using x:

100-x=y

100-15 =y

y=85

So % abundance for the isotope with mass number 50 is 15%, and the % abundance for the isotope with mass number 52 is 85%.