The isotopes Ra-226 undergoes \alpha decay with a half-life of 1620 years. What is the activity of 1\;g of Ra-226? Avogadro number = 6.023 * 10^{23}\; /mole.

Given,
Half life T_{1/2} = 1620 years = 5.1 * 10^{10} Sec
Mass of Ra-226 = 1 gm
Activity of Ra-226\; ; (\frac{dN}{dt}) = \; ?


Now,
\lambda =   \frac{0.693}{5.1 \; * \; 10^{10}} = 1.36 * 10^{-11}\; Sec^{-1}

Again,

           226 gm of Ra-226 contains 6.023 * 10^{23} atoms


           1 gm of Ra-226 contains \frac{6.023 \; * \; 10^{23}}{226} = 2.66 * 10^{21} atoms


           \therefore \;\;\; N= 2.66 * 10^{21} atoms

Now,

           \frac{dN}{dt} = \lambda \,N = 1.36 * 10^{-11} * 2.66 * 10^{10}\; dis/Sec.


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