The decay rate of radium at any time `t` is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.

Answer

` t=log 2/lambda`

Explanation

Let mass =`m`


According to the question,


`(dm)/(dt)prop m`


`(dm)/(dt)=-lambda m`


`(dm)/m=-lambda dt`


Integrating both sides we get,


`int (dm)/m=int -lambda dt`


`rArr logm=-lambda t+c`


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