The isotope of iodine with mass number 128 undergoes beta decay with a half-life of 25.00 minutes. How long will it take for 93.75% of a sample of pure ¹²⁸ I to decay

Question

Quizplus · Accepted Answer

The half-life of iodine-128 is 25.00 minutes, which means that every 25.00 minutes, half of the sample will decay. Using exponential decay formula we can calculate the fraction of the sample that remains after a certain time t:
N(t) = N₀ e^(-λt)
where N(t) is the amount of iodine-128 remaining after time t, N₀ is the initial amount of iodine-128, λ is the decay constant, and e is the base of the natural logarithm.

We can calculate the decay constant as follows:
t₁/₂ = ln(2)/λ
λ = ln(2)/t₁/₂
λ = ln(2)/25.00 min = 0.0278 min⁻¹

Now we can use the fraction remaining to find the amount of time it takes for 93.75% of the sample to decay:
0.9375 = N(t)/N₀ = e^(-λt)
ln(0.9375) = -λt
t = -ln(0.9375)/λ = 100. min (rounded to three significant figures)

Therefore, the answer is C) 100. min

The Isotope of Iodine with Mass Number 128 Undergoes Beta