The mean lives of a radioactive substance are 1620 years and 405 years for-emission and -emission respectively. Find out the time during which three-fourth of a sample will decay if it is decaying both by -emission and-emission simultaneously.



Correct option is

449 years

The decay constants for  emission are respectively  per year. 




After  th part has been disintegrated, 




              = 449 years.



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. . 


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.


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.


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


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.



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.



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.    


A radioactive element of atomic weight 99 has a half-life of 6 hours. Find the activity in a solution containing 1 gram of the element in the beginning. The Avogadro’s number is .   


In an ore containing uranium, the ratio of  nuclei is 3. Calculate the age of the ore, assuming that all the lead present in the ore is the final stable product of . Take the half-life of .


Calculate the energy in joule equivalent to the mass of one proton. The mass of proton is 1.00728 u. Express the energy in kilowatt-hour also.