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Half Life and Average Life

The normal ac...

Question

The normal activity of living carbon-containing matter is found to be about 15 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 (5730 years) 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 civilisation.

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Solution

Decay rate of living carbon-containing matter, R = 15 decay/min

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

Half life of, = 5730 years

The decay rate of the specimen obtained from the Mohenjodaro site:

R' = 9 decays/min

Let N' be the number of radioactive atoms present in the specimen during the Mohenjodaro period.

Therefore, we can relate the decay constant, λand time, t as:

Hence, the approximate age of the Indus-Valley civilisation is 4223.5 years.

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Similar questions

Q. The normal activity of living carbon-containing matter is found tobe about 15 decays per minute for every gram of carbon. This activityarises from the small proportion of radioactive 146 C present with thestable carbon isotope 126 C . When the organism is dead, its interactionwith the atmosphere (which maintains the above equilibrium activity)ceases and its activity begins to drop. From the known half-life (5730years) of 146 C , and the measured activity, the age of the specimencan be approximately estimated. This is the principle of 146C dating used in archaeology. Suppose a specimen from Mohenjodaro givesan activity of 9 decays per minute per gram of carbon. Estimate theapproximate age of the Indus-Valley civilisation.

Q. A wooden box excavated from Indus valley had an activity of

1.18 \times 10^{13}

disintegration per minute per gm. of carbon. What is the approximate age of this civilization?

Q. Carbon-14 is used to determine the age of organic material. The procedure is based on the formation of

^{14} C

by neutron capture in the upper atmosphere.

_{7}^{14} N +_{0}^{1} n \to_{6}^{14} C +_{1} P^{1}

^{14} C

is absorbed by living organisms during photosynthesis. The

^{14} C

content is constant in living organisms once the plant or animal dies, the uptake of carbon dioxide by it ceases and the level of

^{14} C

in the dead being, falls due to the decay which C-14 undergoes

_{6}^{14} C \to_{7}^{14} N + β^{-}

The half-life period of

^{14} C

is 5770 yr.
The decay constant

(λ)

can be calculated by using the following formula

λ = \frac{0.693}{t_{\frac{1}{2}}} .

The comparison of the

β^{-}

activity of the dead matter with that of the carbon still in circulation
enables measurement of the period of the isolation of the material from the living cycle. The
method however, ceases to be accurate over periods longer than 30,000 yr. The proportion of

^{14} C

^{12} C

in living matter is

1 : 10^{12} .

Which of the following option is correct?

Q. A sample of wooden artifact is found to undergo

9

disintegrations per minute per gram of carbon. What is the approximate age of the artifact? The half-life of

_{6}^{14} C

5730

years and radioactivity of wood recently cut is

15

disintegrations per minute per gram of carbon.

Q. Carbon-14 is used to determine the age of organic material. The procedure is based on the formation of

^{14} C

by neutron capture in the upper atmosphere.

_{7}^{14} N +_{0}^{1} n \to_{6}^{14} C +_{1} P^{1}

^{14} C

is absorbed by living organisms during photosynthesis. The

^{14} C

content is constant in living organisms once the plant or animal dies, the uptake of carbon dioxide by it ceases and the level of

^{14} C

in the dead being, falls due to the decay which C-14 undergoes

_{6}^{14} C \to_{7}^{14} N + β^{-}

The half-life period of

^{14} C i s 5770 y r .

The decay constant

(λ)

can be calculated by using the following formula

λ = \frac{0.693}{\frac{t_{1}}{2}} .

The comparison of the

β^{-}

activity of the dead matter with that of the carbon still in circulation
enables measurement of the period of the isolation of the material from the living cycle. The
method however, ceases to be accurate over periods longer than 30,000 yr. The proportion of

^{14} C

^{12} C

in living matter is

1 : 10^{12} .

What should be the age of fossil for meaningful determination of its age?

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