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?

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Answer 1 · 2016-10-20T14:13:10

% abundance of isotope with mass 50: 15%

% abundance of isotope with mass 52: 85%

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

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

$5170 = (x \cdot 50) + ((100 - x) \cdot 52))$ $5170 = (x*50)+((100-x)*52))$

$5170 = 50 x + 5200 - 52 x$ $5170 = 50x+5200-52x$

$5170 = 5200 - 2 x$ $5170 = 5200-2x$

$- 30 = - 2 x$ $-30=-2x$

$x = 15$ $x=15$

Find the value of y using x:

$100 - x = y$ $100-x=y$

$100 - 15 = y$ $100-15 =y$

$y = 85$ $y=85$

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