NEET-XII-Physics
46: The Nucleus
- #25The half-life of 226Ra is 1602 y. Calculate the activity of 0.1 g of RaCl2 in which all the radium is in the form of 226Ra. Taken atomic weight of Ra to be 226 g mol-1 and that of Cl to be 35.5 g mol-1.Ans : Given:
Half-life of radium, T1/2 = 1602 years
Atomic weight of radium = 226 g/mole
Atomic weight of chlorine = 35.5 g/mole
Now,
1 mole of RaCl2 = 226 + 71 = 297 g
297 g = 1 mole of RaCl2
0.1 g = `` \frac{1}{297}\times 0.1\,\mathrm{\,mole\,}\,\mathrm{\,of\,}{\,\mathrm{\,RaCl\,}}_{2}``
Total number of atoms in 0.1 g of RaCl2, N `` =\frac{0.1\times 6.023\times {10}^{23}}{297}=0.02027\times {10}^{22}``
`` ``
∴ No of atoms, N = 0.02027 `` \times `` 1022
`` \,\mathrm{\,Disintegration\,}\,\mathrm{\,constant\,},\lambda =\frac{0.693}{{T}_{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}``
`` =\frac{0.693}{1602\times 365\times 24\times 3600}``
`` =1.371\times {10}^{-11}``
Activity of radioactive sample, A = `` \lambda N``
= `` 1.371\times {10}^{-11}\times 2.027\times {10}^{20}``
= `` 2.8\times {10}^{9}\,\mathrm{\,disintegrations\,}/\,\mathrm{\,second\,}``
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