Obtain the amount of 

   

necessary to provide a radioactive source
of 8.0 mCi strength. The half-life of 

   

is 5.3 years.

Answer –

We are given the strength of the radioactive source as –

   

= 8 x 10^-3 x 3.7 x 10¹⁰

= 29.6 x 10⁷ decay/s

Where,

N is the required number of atoms

Half-life of 

   

is given to us, which is = 5.3 years

Converting the half life time into seconds, we get –

   

= 5.3 × 365 × 24 × 60 × 60

   

= 1.67 × 10⁸ s

We know that the rate of decay for decay constant λ can be written as following –

   

   

Using both relations, we get –

   

N = 7.133 x 10¹⁶ atoms

For 

   

–

Mass of 6.023 × 10²³ atoms = 60 g

Mass of 7.133 x 10¹⁶ atoms will be given by

   

= 7.106 x 10^-6 g

Hence, the amount of 

   

necessary for the purpose is 7.106 × 10⁻⁶ g.