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a radioactive element decays from 300g to 220g in 48 hours. how much of the sample is left after 1 week?

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Final answer:

After using the formula for radioactive decay, we find that approximately 192.65g remains of the radioactive element after 1 week.

Step-by-step explanation:

To solve this problem, we can use the formula for radioactive decay: A = A0 * (1/2)(t / T1/2), where A is the final amount, A0 is the initial amount, t is the time elapsed, and T1/2 is the half-life.

Step-by-step solution:

  • Initial amount, A0 = 300g
  • Final amount, A = 220g
  • Time elapsed, t = 48 hours
  • Half-life, T1/2 = unknown
  • Using the formula A = A0 * (1/2)(t / T1/2), we can write the equation:

220 = 300 * (1/2)(48 / T1/2)

  • Solving for T1/2 gives us T1/2 = 48 * ln(2) / ln(300/220)

Substituting the value of T1/2 into the equation gives us:

A = 300 * (1/2)(t / (48 * ln(2) / ln(300/220)))

  • Calculating the amount after 1 week (7 days) by substituting t = 7 * 24 hours into the equation gives us :

A = 300 * (1/2)(7 * 24) / (48 * ln(2) / ln(300/220)))

  • Calculating the final value of A gives us A = 192.65g

Therefore, after 1 week, approximately 192.65g remains of the radioactive element.

User Jerrod Horton
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