Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
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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 - Physics

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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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Solution 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 Concept: Radioactivity - Introduction of Radioactivity.
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