Physics question-isotope half-life

Archive SAT Subject Test Preparation
1

<p><a href=“http://i584.■■■■■■■■■■■■■■■/albums/ss284/sear_squid/isotopehalflifequestion.png[/url]”>http://i584.■■■■■■■■■■■■■■■/albums/ss284/sear_squid/isotopehalflifequestion.png&lt;/a&gt;&lt;/p&gt;

2

<p>Please, explain this question to me in full detail. Thanks in advance.</p>

3

<p>Reproduced Below:</p>

<p>The half-life of one isotope of radium is about years. In a given sample of this isotope, 15/16 of the radium atoms will decay in a time most nearly equal to:</p>

<p>A- 1,000 years
B- 1,500 years
C- 1,600 years
D- 3,200 years
E- 6,400 years</p>

4

<p>A half-life is the time it takes for 1/2 of the remaining sample to go away. The question asks for how much time it takes for 15/16 to go away, leaving 1/16. 1/16 is 1/(2^4), which means that 4 half-lives pass for 15/16 to decay.</p>

<p>4(half-life time)=4(1600)=6400 years</p>

5

<p>1600 years 8/16
3200 years 12/16
6400 years 14/16 </p>

<p>so E is closest</p>