Chapter 20: Problem 26
A radioactive substance undergoes decay as follows: $$ \begin{array}{cc} \text { Time (days) } & \text { Mass (g) } \\ \hline 0 & 500 \\ 1 & 389 \\ 2 & 303 \\ 3 & 236 \\ 4 & 184 \\ 5 & 143 \\ 6 & 112 \end{array} $$ Calculate the first-order decay constant and the half-life of the reaction.
Short Answer
Step by step solution
Understand the decay model
Use the decay formula
Calculate decay constant \( k \)
Calculate the half-life
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
First-Order Kinetics
- Proportional decay rate
- Exponential decrease over time
- Key contributors: initial mass and decay constant
Decay Constant
- Indicates speed of decay
- Can be calculated using observed data points
- Helpful in isotope identification
Half-Life
- Time for half the sample to decay
- Gives insight into stability of isotopes
- Calculated directly from decay constant
Natural Logarithm
- Translates exponential to linear relationships
- Simplifies solving decay equations
- Essential for k determination and half-life calculations
Radioactive Isotopes
- Serve as tracers in the medical field
- Used for dating ancient artifacts
- Power sources for nuclear reactors and weapons