QuestionMay 27, 2025

Question 23 (Mandatory)(4 points) The first-order decay of radon has a half-life of 3.823 days. How many grams of radon decomposes after 5.55 days if the sample initially weighs 100.0 grams? 50.08 83.4 g ) 63.4 g 16.6 g

Question 23 (Mandatory)(4 points) The first-order decay of radon has a half-life of 3.823 days. How many grams of radon decomposes after 5.55 days if the sample initially weighs 100.0 grams? 50.08 83.4 g ) 63.4 g 16.6 g
Question 23 (Mandatory)(4 points)
The first-order decay of radon has a half-life of 3.823 days. How many grams of radon decomposes after 5.55 days if
the sample initially weighs 100.0 grams?
50.08
83.4 g
) 63.4 g
16.6 g

Solution
4.1(263 votes)

Answer

63.4 g Explanation 1. Calculate the decay constant Use the formula for half-life: **k = \frac{\ln(2)}{t_{1/2}}**. Here, t_{1/2} = 3.823 days. So, k = \frac{\ln(2)}{3.823}. 2. Apply the first-order decay formula Use **N(t) = N_0 e^{-kt}** to find remaining radon. N_0 = 100.0 grams, t = 5.55 days. Substitute k from Step 1. 3. Calculate decomposed radon Subtract remaining radon from initial amount: 100.0 - N(t).

Explanation

1. Calculate the decay constant<br /> Use the formula for half-life: **$k = \frac{\ln(2)}{t_{1/2}}$**. Here, $t_{1/2} = 3.823$ days. So, $k = \frac{\ln(2)}{3.823}$.<br /><br />2. Apply the first-order decay formula<br /> Use **$N(t) = N_0 e^{-kt}$** to find remaining radon. $N_0 = 100.0$ grams, $t = 5.55$ days. Substitute $k$ from Step 1.<br /><br />3. Calculate decomposed radon<br /> Subtract remaining radon from initial amount: $100.0 - N(t)$.
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