# 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?

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:

$51.70 = \frac{\left(x \cdot 50\right) + \left(\left(100 - x\right) \cdot 52\right)}{100}$

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

$5170 = 50 x + 5200 - 52 x$

$5170 = 5200 - 2 x$

$- 30 = - 2 x$

$x = 15$

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%.