#### Question

The half-life of ^{226}Ra is 1602 y. Calculate the activity of 0.1 g of RaCl_{2} in which all the radium is in the form of ^{226}Ra. 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, T_{1}_{/2} = 1602 years

Atomic weight of radium = 226 g/mole

Atomic weight of chlorine = 35.5 g/mole

Now,

1 mole of RaCl_{2} = 226 + 71 = 297 g

297 g = 1 mole of RaCl_{2}

`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