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Question
The 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.
Solution
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" = 1/297 xx 0.1` mole of `"RaCl"_2`
Total number of atoms in 0.1 g of `"RaCl"_2` , N
`= (0.1 xx 6.023 xx 10^23)/297 = 0.02027 xx 10^22`
∴ No of atoms, `N = 0.02027 xx 10^22`
Disintegration constant , `lambda = 0.693/T_(1"/"2)`
`= 0.693/(1602 xx 365 xx 24 xx 3600)`
`= 1.371 xx 10^-11`
Activity of radioactive sample , A = `lambdaN`
`= 1.371 xx 10^-11 xx 2.027 xx 10^20`
`= 2.8 xx 10^9` disintegrations/second
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