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Class 12 Physics Modern Physics Nuclei

A piece of wood from the ruins of an ancient building was found to have a

C^{14}

activity of

12

disintegration per minute per gram of its carbon content. The

C^{14}

activity of the living wood is

16

disintegration per minute per gram. How long ago did the tree, from which the wooden sample came, di? Given half-life of

C^{14}

is

5760

years.

Solution: Rate of disintegration in old wood sample of C-14 radioactive atms is

12

atoms per min gm. Initially rate of distintegration of

C - 14

when the tree was live

= 16

atoms per min per gm.

T_{1 / 2}

of C-14 nuclei

= 5760

years
According to radioactive decay law

= N_{0} e^{- λ t} o r R = R_{0} e^{- λ t}

12 = 16 e^{- λ t} \Rightarrow e^{λ t} = \frac{1 6}{1 2}

lo g_{e} e^{λ t} = lo g_{e} \frac{4}{3}

λ t = lo g_{e} \frac{4}{3}

t = \frac{2 . 3 0 3 \times lo g _{10} \frac{4}{3}}{λ} (∵ λ = \frac{0 . 6 9 3 1}{T _{1 / 2}})

= \frac{2 . 3 0 3 \times ( lo g 4 - lo g 3 ) \times 5 7 6 0}{0 . 6 9 3 1} y e a r

∴ t = \frac{2 . 3 0 3 ( 0 . 6 0 6 0 - 0 . 4 7 7 1 ) 5 7 6 0}{0 . 6 9 3 1} = 2391.20 y e a r s

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solid and semiconductor devices

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necessary to provide a radioactive source of 8.0 mCi strength. The half-life of

_{27}^{60} C o

play button image

A radioactive isotope has a half-life of

T

years. How long will it take the activity to reduce to (a)

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play button image

The rest mass of an electron as well so that of positron is

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play button image

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_{12}^{24} M g

is 78.99% by mass. Calculate the abundances of other two isotopes.

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_{6}^{14} C

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Suppose India had a target of producing by 2020 AD, 200,000 MW of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e. conversion to electric energy) of thermal energy produced in a reactor was 25%. How much amount of fissionable uranium would our country need per year by 2020? Take the heat energy per fission of

^{235} U

to be about 200 MeV.

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