Nuclear Decay Worksheet Answers: Simple & Clear Guide
Table of Contents :
Nuclear decay is a fundamental concept in nuclear chemistry and physics. Understanding the types of nuclear decay, the principles behind it, and how to work through problems is crucial for students and enthusiasts alike. In this guide, we will explore the answers to common nuclear decay worksheet problems, providing clear explanations and examples. Let's dive into the world of nuclear decay! ⚛️
What is Nuclear Decay?
Nuclear decay, also known as radioactive decay, is the process by which an unstable atomic nucleus loses energy by emitting radiation. This can occur in various forms, including alpha decay, beta decay, and gamma decay. Understanding these types of decay is essential for solving related problems.
Types of Nuclear Decay
-
Alpha Decay (α decay): In this type of decay, an atomic nucleus emits an alpha particle, which consists of two protons and two neutrons (essentially a helium nucleus). This process results in a new element that has an atomic number reduced by 2 and a mass number reduced by 4.
- Example:
- Original element: Uranium-238 (₉₂U²³⁸)
- Decay:
- ₉₂U²³⁸ → ₉₀Th²³⁴ + ₂He⁴
- Example:
-
Beta Decay (β decay): In beta decay, a neutron in the nucleus transforms into a proton while emitting a beta particle (an electron) and an antineutrino. This increases the atomic number by 1, while the mass number remains the same.
- Example:
- Original element: Carbon-14 (₆C¹⁴)
- Decay:
- ₆C¹⁴ → ₇N¹⁴ + -₁e⁰
- Example:
-
Gamma Decay (γ decay): Gamma decay involves the release of gamma radiation from a nucleus transitioning from a higher energy state to a lower energy state. This decay does not change the atomic number or mass number.
- Example:
- Original element: Cobalt-60 (₂₇Co⁶⁰)
- Decay:
- ₂₇Co⁶⁰ → ₂₇Co⁶⁰ + γ
- Example:
Nuclear Decay Calculations
To solve nuclear decay problems, it's important to understand how to balance nuclear equations, calculate remaining quantities of a radioactive substance, and apply half-life concepts.
Half-Life
The half-life (t½) of a radioactive isotope is the time it takes for half of the substance to decay.
- Formula:
[
N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}}
]
- (N(t)): Remaining quantity after time (t)
- (N_0): Initial quantity
- (t_{1/2}): Half-life of the substance
- (t): Time elapsed
Example Problem
Suppose you have 100g of a radioactive isotope with a half-life of 5 years. How much will remain after 15 years?
-
Calculate the number of half-lives that have passed:
- (\frac{15 \text{ years}}{5 \text{ years/half-life}} = 3 \text{ half-lives})
-
Apply the half-life formula: [ N(15) = 100g \left( \frac{1}{2} \right)^3 = 100g \times \frac{1}{8} = 12.5g ]
Therefore, after 15 years, 12.5g of the isotope will remain. 🎉
Common Nuclear Decay Problems and Solutions
To further clarify nuclear decay concepts, let’s explore a table of common problems you might encounter on a nuclear decay worksheet along with their answers:
<table> <tr> <th>Problem</th> <th>Answer</th> </tr> <tr> <td>1. Write the decay equation for Uranium-238 undergoing alpha decay.</td> <td>₉₂U²³⁸ → ₉₀Th²³⁴ + ₂He⁴</td> </tr> <tr> <td>2. Calculate the remaining mass of a 200g sample after 4 half-lives (t½ = 3 years).</td> <td>12.5g</td> </tr> <tr> <td>3. What element is formed when Carbon-14 undergoes beta decay?</td> <td>Nitrogen-14 (₇N¹⁴)</td> </tr> <tr> <td>4. How much of a 50g radioactive substance with a half-life of 2 years will remain after 6 years?</td> <td>6.25g</td> </tr> <tr> <td>5. Write the decay equation for Cobalt-60 undergoing gamma decay.</td> <td>₂₇Co⁶⁰ → ₂₇Co⁶⁰ + γ</td> </tr> </table>
Important Notes
- "Always remember to balance the equations properly when dealing with nuclear decay."
- "Different isotopes have unique half-lives, so always check the values when performing calculations."
- "For beta decay, a neutron converts to a proton. This change in particle type is crucial for identifying the new element."
Conclusion
Nuclear decay is a fascinating and essential aspect of nuclear physics and chemistry that impacts everything from energy production to medical applications. Mastering the concepts of alpha, beta, and gamma decay, alongside calculations involving half-lives, allows students to tackle worksheet problems with confidence. Use this guide as a stepping stone to deepen your understanding of nuclear decay and impress your teachers and peers! 🌟