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. .

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.

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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.