Physics Class 12 NCERT Solutions: Chapter 13 Nuclei Part 4

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Formula of radioactivity

Formula of Radioactivity

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Q: 8. The normal activity of living carbon-containing matter is found to be about decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive present with the stable carbon isotope . When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life of , and the measured activity, the age of the specimen can be approximately estimated. This is the principle of dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilization.

Answer:

Decay rate of living carbon-containing matter,

Let N be the number of radioactive atoms present in a normal carbon- containing matter. Half-life of , years,

The decay rate of the specimen obtained from the Mohenjo-Daro site:

Let be the number of radioactive atoms present in the specimen during the Mohenjo-Daro period.

Therefore, we can relate the decay constant, and time, as:

Hence, the approximate age of the Indus-Valley civilization is.

Q: 9. Obtain the amount of necessary to provide a radioactive source of strength. The half-life of is years.

Answer:

The strength of the radioactive source is given as:

Where,

Required number of atoms

Half-life of years

For decay constant, we have the rate of decay as:

Where,

For:

Mass of (Avogadro’s number)

∴Mass of atoms

Hence, the amount of necessary for the purpose is.

Q: 10. The half-life of is 28 years. What is the disintegration rate of of this isotope?

Answer:

Half-life of, years

Mass of the isotope,

of atom contains (Avogadro’s number) atoms.

Therefore, of contains:

number of atoms

Rate of disintegration,

Where,

Decay constant

Hence, the disintegration rate of of the given isotope is