Numerical Based on Decay Constant Problem 13 - Nuclear Chemistry & Radioactivity | Summary and Q&A

TL;DR

Learn how to calculate the percentage of an undecayed sample after a certain period of time for a given radioactive element.

Key Insights

• ☠️ The half-life of a radioactive element determines the rate at which it decays.
• ❓ The decay constant can be calculated using the formula lambda = 0.693 / T_half.
• 🥳 The formula lambda = 2.303 / (log10(M_naught / N)) allows us to find the ratio of the initial amount of the sample to the remaining amount.

Transcript

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Questions & Answers

Q: What is the half-life of the sulfur-35 sample?

The half-life of the sulfur-35 sample is 87.8 days.

Q: What is the formula for calculating the decay constant?

The formula for calculating the decay constant is lambda = 0.693 / T_half, where T_half is the half-life.

Q: What formula is used to find the ratio of the initial amount of the sample to the remaining amount?

The formula used is lambda = 2.303 / (log10(M_naught / N)), where M_naught is the initial amount and N is the remaining amount.

Q: What is the value of N, the remaining amount of the sample, after 180 days?

The value of N is found to be 24.21, representing 24.21% undecayed sample.

Summary & Key Takeaways

• The problem is to find the percentage of sulfur-35 sample that remains undecayed after 180 days, given its half-life of 87.8 days.

• The decay constant is calculated using the formula lambda = 0.693 / T_half, where T_half is the half-life.

• The formula lambda = 2.303 / (log10(M_naught / N)) is used to find the value of N naught / N, which represents the ratio of the initial amount of the sample to the remaining amount.

• By substituting the values and solving the equation, the value of N is found to be 24.21, representing 24.21% undecayed sample.