2) Pd-100 has a half-life of 3.6 days. If one had 6.02 x 10<sup>23</sup> atoms at the start, how many atoms would be present after 20.0 days?

<blockquote>
20.0 / 3.6 = 5.56 half-lives

<P>(1/2)<sup>5.56</sup> = 0.0213 (the decimal fraction remaining after 5.56 half-lives)

<P>(6.02 x 10<sup>23</sup>) (0.0213) = 1.28 x 10<sup>22</sup> atoms remain
</blockquote>

<P>4) After 24.0 days, 2.00 milligrams of an original 128.0 milligram sample remain. What is the half-life of the sample?

<blockquote>
2.00 mg / 128.0 mg = 0.015625

<P>How many half-lives must have elaspsed to get to 0.015625 remaining?

<blockquote>
(1/2)<sup>n</sup> = 0.015625

<br>n log 0.5 = log 0.015625

<br>n = log 0.5 / log 0.015625

<br>n = 6
</blockquote>

24 days / 6 half-lives = 4.00 days (the length of the half-life)

<P><A HREF="http://blip.tv/file/2783560">Video: An Alternate Solution to the Above Problem</A>
</blockquote>

<P>6) How long will it take for a 40.0 gram sample of I-131 (half-life = 8.040 days) to decay to 1/100 its original mass?

<blockquote>
(1/2)<sup>n</sup> = 0.01 (see #2 for the solution technique, 0.01 comes from 1/100 in the problem)

<P>n = 6.64

<P>6.64 x 8.040 days = 53.4 days
</blockquote>

<P>7) Fermium-253 has a half-life of 0.334 seconds. A radioactive sample is considered to be completely decayed after 10 half-lives. How much time will elapse for this sample to be considered gone?

<blockquote>0.334 x 10 = 3.34 seconds</blockquote>

<P>9) 100.0 grams of an isotope with a half-life of 36.0 hours is present at time zero. How much time will have elapsed when 5.00 grams remains?

<blockquote>
5.00 / 100.0 = 0.05 (decimal fraction remaining)

<P>(1/2)<sup>n</sup> = 0.05 (see #2 for the solution technique)

<P>n = 4.32 half-lives

<P>36.0 hours x 4.32 = 155.6 hours
</blockquote>