A160g radioactive sample is left undisturbed for 12.5 hours. at the end of that period, only 5.0g remain. what is the half-life of this sample? show work

2.50 h  

Step-by-step explanation:

The half-life of a sample is the time it takes for half of it to decay.  

After one half-life, half (50 %) of the original amount will remain.  

After a second half-life, half of that amount (25 %) will remain, and so on.  

We can construct a table as follows:  

  No. of      Fraction          Mass

half-lives  remaining   Remaining/g

      1                 ½                  80

      2                ¼                  40

      3                ⅛                  20

      4                ¹/₁₆                 10

      5                ¹/₃₂                 5.0

      6                ¹/₆₄                 2.5

We see that 5.0 g remain after five half-lives.

5t_½ = 12.5 h     Divide each side by 5

 t_½ = 2.50 h

The half-life is 2.50 h.

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