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?

Md Ariful Islam

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Md Ariful Islam

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

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