Calculating time elapsed using the half life of an element?

Question

I'll just give you my homework problem exactly as written:

Assuming a half life of 1599 years, how many years will be needed for the decay of 15/16 of a given amount of radium-226?

How can I answer this without using logarithms?

littlemaster · Accepted Answer

No need to use logarithms.

See, when Ra-226 has been decayed 15/16....life remaining is 1/16

So, the half life of Ra-226 remaining will be 1599 years

So, 1/4 life of Ra-226 remaining will be in 1599x2 years=3198 years

So, 1/8 life of Ra-226 remaining will be in 1599x3 years=4797 years

So, 1/16 life of Ra-226 remaining will be in 1599x4 years=6396 years

You can come to step 4 directly in one step

Calculating time elapsed using the half life of an element?

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