12. Nuclear physics A.md

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Mass Defect and Nuclear Binding Energy

Understanding and Recall: What is the equivalence between energy and mass as represented by E = mc²? Can you recall and use this equation? Answer: The equation E = mc², derived by Albert Einstein, shows the equivalence between energy (E) and mass (m). According to this equation, mass can be converted into energy and vice versa. The 'c' in the equation stands for the speed of light in a vacuum (approximately 3 x 10^8 m/s), and it shows that a small amount of mass can be converted into a large amount of energy.

Representation: White down a simple nuclear equation. And point out all the element meaning. Answer: The nuclear equation representing this reaction is:

¹⁴₇N + ²⁴₂He -> ¹⁷₈O + ¹₁H

Definition and Use: Define the terms mass defect and binding energy and explain how they are used in nuclear physics. Answer:

Mass Defect: It is the difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons. The mass defect arises because some mass is converted into energy to hold the nucleus together.

Binding Energy: This is the energy required to disassemble a nucleus into its separate protons and neutrons. It is equivalent to the energy released when the nucleus was formed. The binding energy is calculated from the mass defect using E=mc².

Sketch: Sketch the variation of binding energy per nucleon with nucleon number. Answer: The graph starts from zero and increases rapidly for small nucleon numbers, reaching a peak at iron (Fe, nucleon number 56). Beyond iron, the graph decreases slowly. This indicates that iron-56 has the most stable nucleus with the highest binding energy per nucleon.

Explanation: What is meant by nuclear fusion and nuclear fission? Answer:

Nuclear Fusion: This is a process where two light nuclei combine to form a heavier nucleus, releasing energy in the process. This is the process that powers the sun and other stars.

Nuclear Fission: This is a process where a heavy nucleus splits into two smaller nuclei, often releasing additional neutrons and a large amount of energy. This process is used in nuclear power plants and atomic bombs.

Explanation: How is the concept of binding energy per nucleon relevant to nuclear reactions, including nuclear fusion and nuclear fission? Answer: The binding energy per nucleon is a measure of the stability of a nucleus. In nuclear fusion, two light nuclei with low binding energy per nucleon combine to form a heavier nucleus with higher binding energy per nucleon, releasing energy. In nuclear fission, a heavy nucleus with lower binding energy per nucleon splits into two lighter nuclei with higher binding energy per nucleon, also releasing energy.

Calculation: Calculate the energy released in a nuclear reaction where the mass defect is 0.005 kg using E = c²∆m. Answer: The energy E released can be calculated as E = c²∆m = (3 x 10^8 m/s)² 0.005 kg = 4.5 x 10^14 J.

Understanding: What evidence do fluctuations in count rate provide about the nature of radioactive decay?Answer: Fluctuations in count rate provide evidence for the random nature of radioactive decay. The number of decays detected per unit of time (count rate) varies due to the fact that each individual nucleus in a sample of radioactive material has an equal chance of decaying at any given time, but exactly when it will decay is unpredictable.

Understanding: What does it mean to say that radioactive decay is both spontaneous and random?Answer: Radioactive decay is spontaneous because it does not need any external influence or trigger - it happens by itself. It is random because it is impossible to predict exactly when a specific nucleus will decay. Each nucleus in a radioactive substance has the same probability of decaying at any time, and this probability does not change over time.

Definition and Recall: Define the terms activity and decay constant, and recall and use the equation A = λN.Answer:

Activity: It is the rate at which a sample of radioactive material decays, measured in becquerels (Bq). One Bq is one decay per second.

Decay Constant (λ): It is the probability per unit time that a nucleus will decay. It is a characteristic of the radioactive isotope and is measured in s⁻¹.

The equation A = λN describes the activity (A) of a sample, where N is the number of undecayed nuclei and λ is the decay constant.

Definition: What is half-life?Answer: The half-life of a radioactive substance is the time taken for half the nuclei in a sample to decay. It is a measure of how quickly a substance decays.

Use: Use the equation λ = 0.693 / t₁/₂ to find the decay constant for a substance with a half-life of 5 years (note: convert the time to seconds).Answer: First, convert 5 years to seconds: 5 years = 5 3.1536 x 10^7 seconds = 1.5768 x 10^8 seconds. Then, use the equation λ = 0.693 / t₁/₂ = 0.693 / 1.5768 x 10^8 seconds = 4.39 x 10^-9 s⁻¹.

Understanding and Use: Explain the exponential nature of radioactive decay, and sketch and use the relationship , where x could represent activity, number of undecayed nuclei, or received count rate.Answer: Radioactive decay is exponential because the rate of decay is proportional to the number of undecayed nuclei, which decreases over time. The equation x = x₀e⁻λt describes this, where x₀ is the initial number of undecayed nuclei (or initial activity or count rate), λ is the decay constant, and t is time. The graph of this equation is a decreasing exponential curve.