Answers

1.  a)  t_1/2 = ln 2 / lambda  so lambda = ln 2 / t _1/2 = 0.693 / (5.3 x 365 x 24 x 3600) = 4.15 x10^-9 s^-1

b) dN/dt = - lambda N   so N =  (dN/dt) / lambda  =  340 / 4.15 x10^-9   = 8.20 x 10¹⁰ atoms

c) 8.20 x 10¹⁰ atoms = 8.20 x 10¹⁰ / 6.02 x 10²³ of a mole, so mass = (8.20 x 10¹⁰ / 6.02 x 10²³) x 60 = 8.17 x 10^-12g

d) 5.3 years = 1 half life so activity = 340/2 = 170 Bq      10.6 years = 2 half lives so 170/2 = 85 Bq

e) 2 years = 63.1 x 10⁶ seconds

         N = N₀  x e ^{-lambda t} 

      so   (dN/dt) = (dN/dt)₀  x e ^{-lambda t}  =  340 x e ^{(- 4.15 x10 ^ -9 x 63.1 x 10 ^ 6)} =  262 Bq

2. a)  204 82  b) 207 85 c) 6 3 d) 24 12