Nuclear Decay Worksheet Answers Key

Nuclear decay is a fascinating and crucial concept in nuclear physics, shedding light on the inherent instability of certain atomic nuclei. Understanding the principles of alpha decay, beta decay, and gamma decay, along with their associated changes in atomic number and mass number, is fundamental for students delving into this subject. These worksheets, designed to solidify comprehension of these topics, often present a variety of problems requiring students to predict the products of nuclear decay reactions, calculate half-lives, and interpret decay equations. Successfully navigating these problems requires not only memorizing the rules but also applying them in a logical and systematic manner. This post aims to provide an answer key for a typical Nuclear Decay Worksheet, along with brief explanations, serving as a helpful resource for both students and educators.

Below, you will find the answers to a typical Nuclear Decay Worksheet. Please note that the specific questions and format may vary depending on the worksheet you are using, but the underlying principles and decay types remain consistent. Before looking at the answers, it is strongly recommended that you attempt the worksheet independently to truly test your understanding. Use this key as a tool for verifying your work and identifying areas that may require further study. Understanding the ‘why’ behind each answer is more important than simply memorizing the solutions.

Alpha Decay

Alpha decay involves the emission of an alpha particle (⁴He₂), which consists of two protons and two neutrons. This reduces the atomic number of the parent nucleus by 2 and the mass number by 4.

Question 1: Write the nuclear equation for the alpha decay of Polonium-210 (²¹⁰Po₈₄).
Answer: ²¹⁰Po₈₄ → ²⁰⁶Pb₈₂ + ⁴He₂
Question 2: Write the nuclear equation for the alpha decay of Uranium-238 (²³⁸U₉₂).
Answer: ²³⁸U₉₂ → ²³⁴Th₉₀ + ⁴He₂
Question 3: What is the daughter nucleus produced when Radium-226 (²²⁶Ra₈₈) undergoes alpha decay?
Answer: ²²²Rn₈₆ (Radon-222)

Beta Decay

Beta decay occurs when a neutron in the nucleus transforms into a proton, emitting a beta particle (an electron, ⁰e_-1) and an antineutrino. This increases the atomic number by 1, while the mass number remains the same.

Question 4: Write the nuclear equation for the beta decay of Carbon-14 (¹⁴C₆).
Answer: ¹⁴C₆ → ¹⁴N₇ + ⁰e_-1 + ν̄_e (antineutrino)
Question 5: Write the nuclear equation for the beta decay of Potassium-40 (⁴⁰K₁₉).
Answer: ⁴⁰K₁₉ → ⁴⁰Ca₂₀ + ⁰e_-1 + ν̄_e (antineutrino)
Question 6: What is the daughter nucleus produced when Strontium-90 (⁹⁰Sr₃₈) undergoes beta decay?
Answer: ⁹⁰Y₃₉ (Yttrium-90)

Gamma Decay

Gamma decay involves the emission of a high-energy photon (gamma ray, γ) from an excited nucleus. This does not change the atomic number or mass number of the nucleus; it simply releases excess energy.

Question 7: Write the nuclear equation for the gamma decay of Cobalt-60m (^60mCo₂₇). The ‘m’ indicates a metastable (excited) state.
Answer: ^60mCo₂₇ → ⁶⁰Co₂₇ + γ
Question 8: A nucleus emits a gamma ray. How do the atomic number and mass number change?
Answer: They remain unchanged.

Half-Life Problems

Half-life (t_1/2) is the time required for half of the radioactive nuclei in a sample to decay.

Question 9: The half-life of Iodine-131 is 8 days. If you start with 100 grams of Iodine-131, how much will remain after 24 days?
Answer: 12.5 grams. (24 days / 8 days/half-life = 3 half-lives. 100g -> 50g -> 25g -> 12.5g)
Question 10: A radioactive isotope has a half-life of 10 years. If a sample initially contains 20 grams of the isotope, how long will it take for the sample to decay to 2.5 grams?
Answer: 30 years. (20g -> 10g -> 5g -> 2.5g. This is 3 half-lives, so 3 * 10 years = 30 years)

This answer key should help you verify your understanding of nuclear decay. Remember to focus on understanding the underlying principles behind each type of decay and how they affect the composition of the nucleus. Good luck with your studies!

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