Half life 10 y. Fraction left after 30 y?

Question

Half life 10 y. Fraction left after 30 y??  
A. ½  
B. ⅓  
C. ¼  
D. ⅛

Accepted Answer

Correct Answer: (D)⅛. 
Rationale: The fraction of the substance left after 30 years is one eighth.Half-life is the time required for half of a radioactive substance to decay. The decay process is exponential, meaning the remaining amount is reduced by half during each half-life period.In this problem, the half-life is 10 years. After 30 years, three half-lives have passed:10 years → first half-life20 years → second half-life30 years → third half-lifeAfter each half-life, the remaining fraction is multiplied by one half.A) ½This fraction corresponds to only one half-life having passed, which is 10 years. Since 30 years have elapsed, more decay has occurred.B) ⅓Radioactive decay does not follow a linear or fractional pattern like thirds. It follows exponential decay based on halves, so this value is not applicable.C) ¼This fraction represents two half-lives, which corresponds to 20 years. After 30 years, an additional half-life has passed, so even less remains.D) ⅛After three half-lives, the remaining fraction is found by multiplying one half by itself three times, which gives one eighth. This correctly represents the amount of substance left after 30 years.ConclusionWith a half-life of 10 years, 30 years corresponds to three half-lives. After three half-lives, one eighth of the original substance remains.

Half life 10 y. Fraction left after 30 y?

A
½

B
⅓

C
¼

D
⅛

The fraction of the substance left after 30 years is one eighth.

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Half life 10 y. Fraction left after 30 y?

A ½ B ⅓ C ¼ D ⅛

The fraction of the substance left after 30 years is one eighth.

Topic Flashcards

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Related Questions

A
½

B
⅓

C
¼

D
⅛