In 420 days, the activity of a sample of polonium (Po) to one-eighth of its initial value. What is the half-life of polonium? Ans. (140 days).



Data Given:


Time taken during the dropping of a sample of polonium (Po) to `\frac{1}{8^{th}}` = 420 days


To Find:



Half-life of a sample of polonium (Po) = ?


Solution:

The quantity of sample of polonium (Po) drops to `\frac{1}{8]^{th}}` of the original quantity after Three Half-lives (3 T₁/₂ ). Hence, 

Time = Number of Half-lives ï½˜ half-life ( T₁/₂ )

or

half-life ( T₁/₂ ) = Time / Number of Half-lives

by putting values

half-life ( T₁/₂ )  = `\frac{420}{3}`

half-life ( T₁/₂ ) = 140 days -----------Ans.