Question

1. A 20g sample of Th-277 decays to 17g in 3 days. What is the rate constant for the decay of this isotope?

a) 1.9 d^-1 b) 0.49 d^-1 c) 1.50 d^-1 d) 0.054 d^-1 e) 0.12 d^-1

2. If two-thirds of a radon-86 sample decays in 6.1 days, what is the half-life of this isotope?

a) 1.18 d b) 0.41 d c) 0.10 d d) 4.2 d e) 3.8 d

Answer 1

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

Where

M_o = initial mass = 20g

M= Mass left after time t = 17 g

t = time = 3 days

k = rate constant = ?

Plug the values we get

k = ( 2.303 /3 )x log (20/17 )

= 0.054 day^-1

Therefore option (d) is correct.

(2) 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 = M_o -(2/3)M_o = (1/3)M_o

t = time = 6.1 days

k = rate constant = ?

Plug the values we get

k = ( 2.303 /6.1 )x log (M_o /[(1/3)M_o ] )

= 0.18 day^-1

We know that half life , t_1/2 = 0.693/k

                                        = 0.693 / 0.18

                                        = 3.8 days

Therefore option (e) is correct.