Question

2) In 1999, the U.S. Environmental Protection Agency set a maximum radon level for drinking water at 4.0 pCi per milliliter.

a. How many decay events occur per second in a milliliter of water for this level of radon radioactivity. 10 points

b. If the above radioactivity were due to the decay of 222Rn (t½ = 3.8 days), how many 222Rn atoms would there be in 1.0 mL of water? 15 points

Answer 1

a) For a mL of water,
number of disintegrations = 4 pCi = 4 * 10^-12 Ci

= 4 * 10^-12 * 3.7 * 10¹⁰ disintegrations/s

= 0.148 disintegrations/s

Part b) write the expression for rate constant.

k = 0.693/t_1/2

here k is rate constant and t_1/2 is half time period.
k = 0.693/3.8 days^-1

k = 0.182 days^-1

  k = 0.182/(3600*24) s^-1

Rate of disintegrations in 1 mL of water = 0.148 * 1

Rate = 0.148 disintegrations/s
rate = kN (N = number of atoms present in 1 mL of water)
0.148 = (0.182/86400 s^-1) * N
N = 0.148 * 86400 / 0.182

N = 0.7 *10^5 atoms