At A Given Instant Are 25% undecayed radioactive Nuclei In A Sample. After 10 Seconds, The Number Of undecayed nuclei Reduces To 12.5%. Calculate The Time In Which The Number Of undecayed nuclei Will Further Reduce To 6.25% Of The Reduced Number.

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Question

At a given instant are 25% undecayed radioactive nuclei in a sample. After 10 seconds, the number of undecayed nuclei reduces to 12.5%. Calculate the time in which the number of undecayed nuclei will further reduce to 6.25% of the reduced number.

Solution

Correct option is

40 seconds

The 6.25% of the reduced number (12.5%) is

         

Suppose, after 10 seconds, the number of undecayed nuclei reduces from 12.5% to 0.78125% in an interval of n half-lives. Then  

        

  

or        n = 4. 

  

                                                        = 40 seconds.

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