1. What is radioactivity ? State the law of radioactive decay. Show that
radioactive decay is exponential in nature.
The half life of radium is 1600 years. How much time does 1 g of radium
take to reduce to 0.125 g.
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Answers
Answer:
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Explanation:
Radioactivity is phenomenon of spontaneous disintegration of nucleus of an atom with emission of one or more radiations. The most common forms of radiation emitted are alpha (\alphaα), beta (\betaβ), and gamma (\gammaγ) radiations.
Law of radioactive decay: According to this law, the rate of decay of radioactive atoms at any instant is directly proportional to the number of atoms present at that instant.
\dfrac{dN}{dt} \propto NdtdN∝N
\dfrac{dN}{dt} = \lambda NdtdN=λN
where NN is number of integrated nucleus present in the sample at any time t and \lambdaλis decay constant.
By integrating the above equation,
\int \dfrac{dN}{N} = \int \lambda t∫NdN=∫λt
ln N = \lambda t + ClnN=λt+C
N=N_0 \space e^{\lambda t}N=N0 eλt
where N_0N0 is original amount.
Therefore, radioactive decay is exponential in nature.
Initial mass of Radium = 1g=1g
Final mass of Radium =0.125g=0.125g
Half life t_{1/2}=1600t1/2=1600 years
The quantity remaining 'n' lifes is \dfrac{1}{2^n}2n1 of initial quantity. So,
\dfrac{1}{2^n} = \dfrac{Final \space mass}{Initial \space mass} \\= \dfrac{0.125}{1} = \dfrac{1}{8} = \dfrac{1}{2^3}2n1=Initial massFinal mass=10.125=81=231
\therefore n = 3∴n=3
Now, time takes = n \times t_{1/2} = 2 (1600) = 4800=n×t1/2
Answer:
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