Question

Barium – 122 has a half-life of 2 minutes. Suppose you obtain a sample weighing 10.0 g and it takes 10 minutes to set up an experiment. How many grams of Barium – 122 will remain at the point when you begin the experiment?

Answer 1

All nuclear reactions are of first order reactions.

For a first order reaction rate constant ,

k = ( 2.303 /t )x log ( Mo / M)
Where
Mo = initial mass= 10.0 g
M= Mass left after time t = ?
t = time = 10 min

k= rate constant= 0.693/half life

= 0.693/2 min

= 0.3465 min^-1

Plug the values we get log(Mo/M) = (kt)/2.303

= (0.3465*10)/2.303

= 1.504

Mo/M=10^1.504 = 31.9

M= 10.0g/31.9

= 0.313 g

So mass of Barium-122 left is 0.313g