Radioactive Decay Worksheet Answers: Your Complete Guide
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Radioactive decay is a fascinating and critical concept in nuclear physics and chemistry, encompassing the process by which unstable atomic nuclei lose energy by emitting radiation. Understanding this phenomenon is essential for various fields, including environmental science, medicine, and nuclear energy. In this article, we will delve into the concept of radioactive decay, explore common types of decay, and provide a comprehensive guide to answering radioactive decay worksheet questions.
What is Radioactive Decay? π
Radioactive decay is the process through which an unstable atomic nucleus loses energy. This process can result in the emission of particles such as alpha particles, beta particles, and gamma rays. The overall goal of radioactive decay is to achieve a more stable atomic configuration.
Types of Radioactive Decay π¬
There are several common types of radioactive decay, including:
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Alpha Decay (Ξ±): Involves the emission of alpha particles (helium nuclei), which consist of two protons and two neutrons. This type of decay typically occurs in heavy elements, such as uranium or radium.
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Beta Decay (Ξ²): Occurs when a neutron in the nucleus transforms into a proton and emits a beta particle (an electron or positron). This type of decay is commonly seen in elements with a high neutron-to-proton ratio, such as carbon-14.
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Gamma Decay (Ξ³): Involves the emission of gamma rays, which are high-energy electromagnetic radiation. Gamma decay often accompanies alpha and beta decay as a way for the nucleus to shed excess energy.
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Positron Emission: A type of beta decay where a proton is converted into a neutron, resulting in the emission of a positron (the antimatter counterpart of an electron).
The Decay Constant and Half-Life β³
Key terms associated with radioactive decay include:
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Decay Constant (Ξ»): A probability value that represents the likelihood of a decay event occurring over a certain period. The decay constant is unique to each radioactive isotope.
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Half-Life (tβ/β): The time it takes for half of the radioactive nuclei in a sample to decay. Each isotope has its specific half-life, which can range from fractions of a second to billions of years.
Hereβs a table summarizing some common isotopes, their decay modes, and half-lives:
<table> <tr> <th>Isotope</th> <th>Decay Mode</th> <th>Half-Life</th> </tr> <tr> <td>Uranium-238</td> <td>Alpha Decay</td> <td>4.5 billion years</td> </tr> <tr> <td>Carbon-14</td> <td>Beta Decay</td> <td>5,730 years</td> </tr> <tr> <td>Radon-222</td> <td>Alpha Decay</td> <td>3.8 days</td> </tr> <tr> <td>Potassium-40</td> <td>Beta Decay</td> <td>1.25 billion years</td> </tr> </table>
Solving Radioactive Decay Problems π
When faced with radioactive decay worksheet questions, understanding the concepts of decay constant and half-life is crucial. Here are some essential formulas:
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Decay Formula: [ N(t) = N_0 e^{-\lambda t} ] Where:
- (N(t)) = remaining quantity of the substance at time (t)
- (N_0) = initial quantity of the substance
- (e) = base of natural logarithm
- (\lambda) = decay constant
- (t) = time elapsed
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Half-Life Formula: [ N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} ] Where:
- (t_{1/2}) = half-life of the substance
Common Worksheet Questions and Answers π
Here are examples of typical questions you might encounter on a radioactive decay worksheet, along with their respective solutions.
Example 1: Half-Life Calculation
Question: If the half-life of Carbon-14 is 5,730 years, how much of a 10 mg sample will remain after 17,190 years?
Solution: [ N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} ]
- (N_0 = 10 , \text{mg})
- (t = 17,190 , \text{years})
- (t_{1/2} = 5,730 , \text{years})
Calculate: [ N(t) = 10 \left(\frac{1}{2}\right)^{\frac{17,190}{5,730}} = 10 \left(\frac{1}{2}\right)^3 = 10 \cdot \frac{1}{8} = 1.25 , \text{mg} ]
Example 2: Remaining Quantity Calculation
Question: A sample of Uranium-238 has a mass of 80 grams. After 9.0 billion years (two half-lives), how much remains?
Solution: Using the half-life of Uranium-238 (4.5 billion years): [ N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} = 80 \left(\frac{1}{2}\right)^{\frac{9.0 , \text{billion}}{4.5 , \text{billion}}} = 80 \left(\frac{1}{2}\right)^{2} = 80 \cdot \frac{1}{4} = 20 , \text{grams} ]
Important Notes π
- Ensure that you identify the correct decay mode for the isotope in question.
- Familiarize yourself with the half-lives of common isotopes, as they frequently appear in problems.
- Practice with various worksheet examples to strengthen your understanding and problem-solving skills.
In summary, understanding radioactive decay, its types, and related calculations will greatly enhance your ability to tackle worksheet questions effectively. Whether for academic purposes or personal interest, mastering this topic is an essential endeavor in the field of science.