A radioactive isotope has a half-life of 20 years. How many grams of a 6 gram sample will remain after 40 years?

Question

A radioactive isotope has a half-life of 20 years. How many grams of a 6 gram sample will remain after 40 years??  
A. 8g  
B. 6g  
C. 3g  
D. 1.5g

Accepted Answer

Correct Answer: (D)1.5g. 
Rationale: 1.5 grams will remain after 40 years.Radioactive decay follows a predictable pattern based on half-life, which is the time required for half of a radioactive substance to decay. In this case, the isotope has a half-life of 20 years, and the initial mass of the sample is 6 grams.After the first half-life (20 years), half of the original 6 grams decays, leaving 3 grams. After the second half-life (40 years total), half of the remaining 3 grams decays, leaving 1.5 grams. This means that after two half-lives, one-quarter of the original sample remains.A. 8 gRadioactive substances do not increase in mass over time. An increase would contradict the nature of radioactive decay.B. 6 gThis would indicate that no decay occurred over 40 years, which is impossible given that two half-lives have passed.C. 3 gThree grams would be the amount remaining after only one half-life (20 years), not after two half-lives.D. 1.5 gThis is correct. After two half-lives, the remaining mass is one-quarter of the original amount. One-quarter of 6 grams is 1.5 grams.ConclusionOver a period of 40 years, the radioactive sample undergoes two half-lives, reducing its mass by half twice. As a result, only one-quarter of the original 6-gram sample remains, which corresponds to 1.5 grams.

A radioactive isotope has a half-life of 20 years. How many grams of a 6 gram sample will remain after 40 years?

A
8g

B
6g

C
3g

D
1.5g

1.5 grams will remain after 40 years.

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A radioactive isotope has a half-life of 20 years. How many grams of a 6 gram sample will remain after 40 years?

A 8g B 6g C 3g D 1.5g

1.5 grams will remain after 40 years.

Topic Flashcards

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Related Questions

A
8g

B
6g

C
3g

D
1.5g