QuestionAugust 25, 2025

Selenium -83 has a half-life of 25.0 minutes. How many minutes would it take for 31/32 of the sample to decay? 125 minutes 32 minutes 100 minutes 83 minutes

Selenium -83 has a half-life of 25.0 minutes. How many minutes would it take for 31/32 of the sample to decay? 125 minutes 32 minutes 100 minutes 83 minutes
Selenium -83 has a half-life of 25.0 minutes. How many minutes would it take
for 31/32 of the sample to decay?
125 minutes
32 minutes
100 minutes
83 minutes

Solution
4.6(209 votes)

Answer

125 minutes Explanation 1. Determine the fraction remaining If 31/32 decays, then 1/32 remains. 2. Use the half-life formula The formula for decay is N = N_0 \left(\frac{1}{2}\right)^{t/T}, where N/N_0 = 1/32, T = 25 minutes. 3. Solve for time t Set \left(\frac{1}{2}\right)^{t/25} = 1/32. Since 1/32 = (1/2)^5, equate exponents: t/25 = 5. 4. Calculate t t = 5 \times 25 = 125 minutes.

Explanation

1. Determine the fraction remaining<br /> If $31/32$ decays, then $1/32$ remains.<br /><br />2. Use the half-life formula<br /> The formula for decay is $N = N_0 \left(\frac{1}{2}\right)^{t/T}$, where $N/N_0 = 1/32$, $T = 25$ minutes.<br /><br />3. Solve for time $t$<br /> Set $\left(\frac{1}{2}\right)^{t/25} = 1/32$. Since $1/32 = (1/2)^5$, equate exponents: $t/25 = 5$.<br /><br />4. Calculate $t$<br /> $t = 5 \times 25 = 125$ minutes.
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