Half life chemistry question ?

Question

Iodine 131 has a half life of 8 days and it decays emitting one of beta rays per mol of iodine 131. If you inject 0.001 moles of iodine 131 into someone , and monitor them for 8 days , how many moles of beta Rays will you detect ? How many beta Rays is this?

Answer 1

If N(0) is the initial amount of iodine 131, t is the elapsed time, t1/2 is the half life of iodine 131, and N(t) is the amount of iodine 131 left after the elapsed time, you get the equation for exponential decay:

 

N(t) = N(0) * (1/2)^[t/(t1/2)] = 0.001mol * (1/2)^[8days / 8days] = 0.001mol * (1/2)^1 = 0.001mol * 1/2 = 0.0005mol

(This checks out since half of the sample would decay during one half life)

 

Amount of iodine 131 that decayed = N(0) - N(t) = 0.001mol - 0.0005mol = 0.0005mol

 

Set up proportion to see how many moles of beta rays are emitted:

 

 1mol beta ray              x mol beta rays

________________   =     ___________________

1mol iodine 131         0.0005mol iodine 131

 

x mol beta rays * 1mol iodine 131 = 1mol beta ray * 0.0005mol iodine 131

x mol beta rays  = (1mol * 0.0005mol) / 1mol = 0.0005 mol beta rays

 

Set up another proportion with Avogadro's number to find the number of beta rays emitted:

Avogadro's number = 6.02 x 10^23 molecules / mol

 

6.02 x 10^23 beta rays         x beta rays

_______________________   =   _____________

         1mol                            0.0005mol

 

x beta rays * 1mol = 6.02x10^23 beta rays * 0.0005mol

x beta rays = (6.02x10^23 beta rays * 0.0005mol) / 1mol = 3.01 x 10^20 beta rays