Chapter 43: Problem 21
The common isotope of uranium, \(^2$$^3$$^8\)U, has a halflife of 4.47 \(\times\) 10\(^9\) years, decaying to \(^2$$^3$$^4\)Th by alpha emission. (a) What is the decay constant? (b) What mass of uranium is required for an activity of 1.00 curie? (c) How many alpha particles are emitted per second by 10.0 g of uranium?
Short Answer
Step by step solution
Calculate the decay constant
Calculate mass of uranium required for an activity of 1.00 curie
Calculate alpha emissions from 10 g of uranium per second
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Uranium-238
This isotope is important in various scientific fields, such as geology and nuclear physics, because of its long half-life. This property makes it useful for dating ancient rocks and for understanding the age of the Earth.
- Characteristics: Uranium-238 has an atomic mass of 238 units, which mainly contributes to its heavy nature.
- Natural Abundance: It accounts for over 99% of the uranium found in nature.
- Applications: Apart from geological dating, Uranium-238 can be used in nuclear reactors, albeit not as a primary fuel, due to its non-fissile nature.
Decay Constant
- Relationship with Half-life: The decay constant is inversely proportional to the isotope's half-life. The equation \( \lambda = \frac{\ln(2)}{t_{1/2}} \) links them directly.
- Determination: In the case of Uranium-238, its decay constant can be calculated if the half-life is known, giving insights into its decay rate.
Understanding the decay constant allows scientists to quantify the stability of an isotope. A small decay constant, such as that of Uranium-238, indicates slow decay, aligning with its long half-life.
Half-life
- Significance: The half-life can be used to date ancient geological formations because it provides a measure of time over which uranium has been decaying.
- Calculation: Given the half-life, scientists can determine how long it will take for half of a uranium sample to change into thorium, making it a powerful tool in geochronology.
- Measurement: The half-life is unaffected by external conditions such as temperature or pressure, making it a reliable constant for scientific calculations.
This constancy allows Uranium-238 to serve as a natural clock, helping us estimate the timing of events in Earth's history.
Alpha Emission
This process reduces the atomic mass and atomic number of the original element, leading to the formation of a new element.
- Consequences for Uranium-238: As Uranium-238 undergoes alpha emission, it loses an alpha particle and is converted into Thorium-234.
- Significance: Alpha particles are heavily charged and relatively massive, meaning they have low penetration power but can cause significant damage if they interact with other matter.
Understanding alpha emission is vital for various applications, including the safe handling of radioactive materials and the design of radiation shielding. The knowledge of emission rates also aids in determining the activity of uranium samples and their potential uses in scientific and industrial fields.