Question

Radioactive decay follows first-order kinetics. If a sample of I-131 decays from 25.0 mg to 8.25 mg in 12.8 days, what is the rate constant, k?

Answer 1

k = 0.0866 days⁻¹

Step-by-step explanation:

The isotope decay of the atom follows the equation:

ln [A] = -kt + Ln[A]₀

Where [A] is the amount of the isotope after time t = 8.25mg

Time = 12.8days

k is rate constant

[A]₀ is actual amount of the isotope = 25.0mg

Replacing:

ln 8.25mg = -k*12.8days + ln 25.0mg

2.11 - 3.22 = -k*12.8days

-1.11 = -k12.8days

k = 0.0866 days⁻¹