Iodine-131 is a radioactive isotope that is used to diagnose and treat some forms of thyroid cancer. Iodine-131 decays to xenon-131 according to the equation: I-131⟶Xe-131+electron The decay is first-order with a rate constant of 0.138 d−1. How many days will it take for 90% of the iodine−131 in a 0.500 M solution of this substance to decay to Xe-131?

16.6 days will it take for 90% of the iodine - 131 in a 0.500 M solution of this substance to decay to Xe-131.

Explanation:

                 I- 131 → Xe - 131 + e⁻

the decay process follow first order kinetics

given, decay constant (λ)= 0.138 d⁻¹

----------------------------------(1)

No → Initial amount of I- 131 = 0.5 (M)

from equation 1

∴ 16.6 days will it take for 90% completion.