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After three half-lives, a sample contains 20 grams of parent isotopes. How many grams of the parent isotope were present to start?

Verified Answer :

PhyCS

Three half lives meant that the mass was halved three times. Therefore, 20 2 2 * 2 to reverse the process yields 160 grams in the beginning.

Answer: 160 g

Explanation:

To calculate we use the formula:

\(a=\frac{a_o}{2^n}\)

where,

a = amount of reactant left after n-half lives = 20 g

\(a_o\) = Initial amount of the reactant = ?

n = number of half lives  = 3

Putting values in above equation, we get:

\(20g=\frac{a_0}{2^3}\)

\(20g=\frac{a_0}{8}\)

\(a_o=8\times 20g=160g\)

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