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

Answer:

% 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%.