Question at position 1 Radioactive iodine-131 has a half-life of 8.0 days. What is the rate constant for the first-order decay of this radioactive isotope? 0.087/day 0.12/day 0.032/day 0.55/day 0.67/day单项选择题
A
0.087/day
B
0.12/day
C
0.032/day
D
0.55/day
E
0.67/day

Question

Question at position 1 Radioactive iodine-131 has a half-life of 8.0 days. What is the rate constant for the first-order decay of this radioactive isotope? 0.087/day 0.12/day 0.032/day 0.55/day 0.67/day单项选择题

A

0.087/day

B

0.12/day

C

0.032/day

D

0.55/day

E

0.67/day

BlackTom AI · Accepted Answer

For first-order radioactive decay the relationship between the decay constant k and the half-life t1/2 is k = ln(2) / t1/2. This comes from N = N0 e^{-kt}; at half-life N/N0 = 1/2 so ln(1/2) = -k t1/2 ⇒ k = ln(2)/t1/2.

Apply the formula with t1/2 = 8.0 days:
1) ln(2) = 0.693147...
2) k = 0.693147... / 8.0
3) k = 0.0866434... day^-1

Rounding to the precision implied by the given half-life (8.0 has two significant figures) gives k ≈ 0.087 day^-1. Units are day^-1 (inverse time), appropriate for a first-order rate constant.

Check: using k = 0.087 day^-1, t1/2 = ln(2)/k = 0.693147/0.087 ≈ 7.97 days ≈ 8.0 days, confirming consistency.

Why the other choices are incorrect:
- 0.12 day^-1 would imply t1/2 = 0.693/0.12 ≈ 5.8 days (not 8.0 days).
- 0.032 day^-1 would imply t1/2 ≈ 21.7 days (much longer than 8.0 days).
- 0.55 day^-1 gives t1/2 ≈ 1.26 days (far too short).
- 0.67 day^-1 gives t1/2 ≈ 1.03 days (also far too short).

Therefore the correct rate constant for iodine-131 with an 8.0-day half-life is 0.087/day, matching the provided answer.

Question at position 1 Radioactive iodine-131 has a half-life of 8.0 days. What is the rate constant for the first-order decay of this radioactive isotope? 0.087/day 0.12/day 0.032/day 0.55/day 0.67/day单项选择题

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