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.

Answer 1

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 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