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**TOPIC
17: Atomic Physics**

**Tip 1:**

In radioactivity, the
Half-Life *T*_{½} is the expected time taken for half the radioactive nuclei to
decay.

For example, if *T*_{½}
is 3 hours and we started off with only 32 radioactive nuclei. After 3
hours, we will be left with 16; after another 3 hours (ie. total 6 hours), we
will be left with 8; after yet another 3 hours (ie. total 9 hours), we will be
left with 4 radioactive nuclei, and so on.

The general formula to compute the number of radioactive nuclei remaining is:

*N* = *N*_{o} (½)^{n}

where *N* is the number of
radioactive nuclei remaining; *N*_{o} the number initially; "*n*"
the number of
Half-Lives, ie. *n* = *t*/*T*_{½}
where *t* is the time that has elapsed.

Using the same example as
above, when the time elapsed was 6 hours, then *n* = 6/3 = 2.

*N* = *N*_{o} (½)* ^{n}*
= 32 (½)

This formula is especially
useful if the time "*t*" is less than one Half-Life, eg. 2 hours.
Then, *n* = 2/3 = 0.667

*N* = *N*_{o} (½)* ^{n}*
= 32 (½)

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