Question

32P is a radioactive isotope with a half-life of 14.3 days. If you currently have 54.7 g of 32P , how much 32P was present 2.00 days ago?

Answer 1

Half life period- is the time taken by a substance to get decayed to half of its original amount. If the original amount of any compound is x g, then after half life period, the decayed amount is x/2 g and rest left = x/2 g

Now here given- half-life (t_1/2 ) = 14.3 days

current amount = [A] = 54.7 g

Initial amount = [A₀] = 54.7 * 2 = 108.4 g

time to be calculated (t) = 2.00 days ago

= 14.3 - 2 = 12.3 days

Now the formula used her is -    k = 0.693 / t_1/2

where k = radioactive decay constant

Thus k = 0.693 /14.3 days

= 0.048 days^-1

Again at time = 12.3 days, the amount of 32P left [A] left cann be calculated y the formula-

2.303 log ([A₀]/ [A]) = kt

Now putting the values-  2.303 log (108.4 g/ [A]) = 0.048 days^-1 * 12.3 days

   2.303 log (108.4 g/ [A]) = 0.59

log (108.4 g/ [A]) = 0.59 / 2.303

   log (108.4 g/ [A]) = 0.025

108.4 g/ [A] = 10^0.025

= 1.059

[A] = 108.4 g / 1.059

= 102.36 g

Thus amount of  32P was present 2.00 days ago = 102.36 g