Q. 1395.0( 1 Vote )
A half-life is the amount of time that it takes for a radioactive substance to decay to one half of its original quantity. Suppose radioactive decay causes 300 grams of a substance to decrease to 300 × 2–3 grams after 3 half-lives. Evaluate 300 × 2–3 to determine how many grams of the substance are left.
Explain why the expression 300 × 2–n can be used to find the amount of the substance that remains after n half-lives.
Answer :
Given, 300 grams of a substance decrease to 300 × 2-3 after 3 half-lives.
⇒ Evaluating 300 × 2-3
We know by laws of exponents, a-n = 
⇒ 300 × 2-3 = 
= 
= 
= 37.5 grams
∴ 3.75 grams of the substance are left.
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