Question

The isotopes  occur in nature in the ratio 140 : 1. Assuming that at the time of earth’s formation they were present in equal ratio, make an estimation of the age of the earth. The half-lives of  respectively.

   

Solution

Correct option is

Let the number of atoms of  at present be N1 and N2respectively. From the formula , we have 

         

Because N0 is same for both (given)

           

           

Where T1 and T2 are half-lives of  respectively. Putting the given values : 

       

          

          .       

SIMILAR QUESTIONS

Q1

The half-life of  against . Calculate the activity of 1 g sample of . Avogadro’s number is .

Q2

The half-life of  is 28 years. How much is the disintegration rate of 15 mg of this isotope? The Avogadro’s number is .

Q3

1 g of particles per second. Find its half-life and average life. Avogadro’s number is .

Q4

Determine the amount of  required to provide a source of -particles of 5 millicurie strength. The half-life of Po is 138 days. The Avogadro’s number is 

Q5

The disintegration rate of a certain radioactive sample at any instant is 4750 disintegrations per minute. 5 minute after, the rate becomes 2700 disintegrations per minute. Calculate the half-life of the sample. . 

Q6

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.

Q7

The normal activity of a living mater containing radioactive carbon C14 is found to be 15 decays per minute per gram of carbon. An archaeological specimen shows an activity of 9 decays per minute per gram of carbon. Estimate the age of the specimen. The half-life of C14 is 5730 years.

Q8

A radioactivity sample contains 2.2 mg of pure  which has half-life period of 1224 seconds. Calculate the number of atoms present initially.

Q9

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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Q10

A radioactive isotope X has a half-life of 3 seconds. At t = 0 second, a given sample of this isotope X contains 8000 atoms. Calculate the number of decays per second in the sample at t = t1 second.