11.44 years it will take for the 1.10 mg sample of pu−236 to decay to 0.140 mg.
Half life time is the time in which concentration of reactant becomes half of the initial concentration.
Total time for the decomposition of pu-236 to 0.140mg is calculated as:
T = (t)ⁿ, where
t = half life time = 2.86 years (given)
n = no. of half life time required
1.1/2 → 0.7 .......... 2.86 yrs (1st half life)
0.7/2 → 0.45 .......... 5.72 yrs (2nd half life)
0.45/2 → 0.225 ..... 8.58 yrs (3rd half life)
0.225/2 → 0.1125 ... 11.44 yrs(4th half life)
Here, n = 4
T = (2.86)⁴ = 11.44 years
Hence, we require little more time than 11.44 years.
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