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Question 8 of 36

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SAT Subject Test

The half-life of one isotope of radium is about text 1,600 end text years. In a given sample of this isotope, 15 divided by 16 of the radium atoms will decay in a time most nearly equal to

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text 1,000 end text years

Correct Answer: 
No

text 1,500 end text years

Correct Answer: 
No

text 1,600 end text years

Correct Answer: 
No

text 3,200 end text years

Correct Answer: 
No

text 6,400 end text years

Correct Answer: 
Yes

During each half-life, an average of 1 divided by 2 of the nuclei present will decay. So after one half-life only about 1 divided by 2 of the radium nuclei remain. After two half-lives the sample contains 1 divided by 2 of 1 divided by 2 , or about 1 divided by 4 of the original number of radium nuclei. In general, the number of nuclei remaining after n half-lives have elapsed isleft parenthesis 1 divided by 2 right parenthesis to the power of n end exponent.Having 15 divided by 16 of the radium nuclei decay means having 1 divided by 16 of them remain, which is left parenthesis 1 divided by 2 right parenthesis to the power of 4 end exponent. So the answer is four half-lives, which is text 6,400 end text years.

Question Difficulty: 
easy