Question

What is the half-life of aluminum-25 if 28.6 seconds are required for the activity of a sample of aluminum-25 to fall to 6.35 percent of its original value?

____sec

Answer 1

For a first order reaction rate constant , k = ( 2.303 /t )x log ( M_o / M)

Where

M_o = initial mass

M= Mass left after time t = (6.35/100)xM_o = 0.0635 M_o

t = time = ?

k = rate constant = 0.693 / t_1/2 = 0.693 / 28.6 s

                          = 0.0242 s^-1

Plug the values we get

t = ( 2.303 /k )x log ( M_o / M)

= ( 2.303x0.0242) x log(M_o / 0.0635M_o)

= 114 s

Therefore the required time is 114 s