A Small Quantity Of Solution Containing  radionuclide (half-life 15 Hours) Of Activity 1.0 microcurie is Injected Into The Blood Of A Person. A Sample Of The Blood Of Volume 1 Cm3 taken After 5 Hours Show An Activity Of 296 Disintegrations Per Minute. Determine The Total Volume Of Blood In The Body Of The Person. .

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Question

A small quantity of solution containing  radionuclide (half-life 15 hours) of activity 1.0 microcurie is injected into the blood of a person. A sample of the blood of volume 1 cm3 taken after 5 hours show an activity of 296 disintegrations per minute. Determine the total volume of blood in the body of the person.

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Solution

Correct option is

If N0 be the initial mass (or no. of radionuclide) of a radioactive material, then the mass remaining after n half-lives is given by

         

The activity R is proportional to N, and so    

             

Here R0 = 1.0 microcurie = 10–6 curie

                

  

  

             

This is the activity in the blood after 5 hours. 

Now,  disintegrations/s are observed in 1 cm3 of blood. Therefore, the volume of the blood showing  is 

       

                                                              .

Testing

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