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How much of a 849 gram sample of Potassium-42 will remain after 62 hours?

Quizzma Team

Potassium-42 has a half life of 12.4 hours. How much of a 849 gram sample of Potassium-42 will remain after 62 hours? (answer will be in grams)




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    1 Answer

    1. Quizzma Team

      To find out how much of a 849 gram sample of Potassium-42 will remain after 62 hours, we can use the formula for exponential decay based on half-lives.

      1. Calculate the number of half-lives that have passed in 62 hours:

      – Half-life of Potassium-42 = 12.4 hours

      – Number of half-lives = Total time / Half-life

      – Number of half-lives = 62 hours / 12.4 hours ≈ 5

      2. Use the half-life to find the remaining amount:

      – The formula for the remaining amount after ( n ) half-lives is:

      [ text{Remaining amount} = text{Initial amount} times left(frac{1}{2}right)^n ]

      – Plug in the values:

      [ text{Remaining amount} = 849 , text{grams} times left(frac{1}{2}right)^5 ]

      – (left(frac{1}{2}right)^5 = frac{1}{32})

      – Therefore:

      [ text{Remaining amount} = 849 , text{grams} times frac{1}{32} approx 26.53 , text{grams} ]

      So, after 62 hours, approximately 26.53 grams of

    3. Quizzma Team

      To calculate the remaining amount of Potassium-42 after 62 hours, we can use the formula for radioactive decay:

      [ N = N_0 left( frac{1}{2} right)^{frac{t}{t_{1/2}}} ]

      Where:

      – ( N ) is the remaining amount,

      – ( N_0 ) is the initial amount (849 grams),

      – ( t ) is the total time elapsed (62 hours),

      – ( t_{1/2} ) is the half-life (12.4 hours).

      1. First, calculate how many half-lives fit into 62 hours:

      [ frac{62 text{ hours}}{12.4 text{ hours/half-life}} approx 5 text{ half-lives} ]

      2. Now, substitute into the formula:

      [ N = 849 left( frac{1}{2} right)^{5} ]

      3. Calculate ( left( frac{1}{2} right)^{5} ):

      [ left( frac{1}{2} right)^{5} = frac{1}{32} ]

      4. Now calculate the remaining amount:

      [ N = 849 times frac{1}{32} approx 26.53 text{ grams} ]

      So, after 62 hours

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