## Question

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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 .

### Solution

Correct option is

All the lead present in the ore is the final stable product of . It means that the number of nuclei of present is equal to the number of nuclei of decayed.

Let the number nuclei of be *N*. Then, the number of nuclei of present in the ore is 3*N*.

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If, in a radioactive substance, initially and after the time *t*, the number of nuclei be *N*_{0} and *N*’ respectively, then

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#### SIMILAR QUESTIONS

Q2

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. .

Q3

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.

Q4

The normal activity of a living mater containing radioactive carbon C^{14} 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 C^{14} is 5730 years.

Q5

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

Q6

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 cm^{3} taken after 5 hours show an activity of 296 disintegrations per minute. Determine the total volume of blood in the body of the person.

.

Q7

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.

Q8

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* = *t*_{1} second.

Q9

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 .