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Ch 43: Nuclear Physics
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Young & Freedman Calc 15th EditionCh 43: Nuclear Physics문제 6
42장, 문제 6

The most common isotope of uranium, 92238U_{92}^{238}U, has atomic mass 238.050788238.050788 u. Calculate (a) the mass defect; (b) the binding energy (in MeV); (c) the binding energy per nucleon.

검증된 단계별 안내
1
Step 1: Understand the problem. The mass defect is the difference between the mass of the nucleus and the sum of the masses of its individual protons and neutrons. The binding energy is the energy equivalent of the mass defect, and the binding energy per nucleon is the binding energy divided by the total number of nucleons.
Step 2: Calculate the total mass of the individual nucleons. The nucleus of 238 92U contains 92 protons and 238 - 92 = 146 neutrons. Use the mass of a proton (1.007276 u) and the mass of a neutron (1.008665 u) to compute the total mass of the nucleons: \( \text{Total mass of nucleons} = 92 \times 1.007276 + 146 \times 1.008665 \).
Step 3: Compute the mass defect. The mass defect is the difference between the total mass of the nucleons and the actual mass of the nucleus: \( \text{Mass defect} = \text{Total mass of nucleons} - \text{Atomic mass of uranium nucleus} \).
Step 4: Convert the mass defect to energy using Einstein's equation \( E = \Delta m c^2 \). Since 1 u corresponds to 931.5 MeV/c^2, the binding energy can be calculated as \( \text{Binding energy} = \text{Mass defect} \times 931.5 \).
Step 5: Calculate the binding energy per nucleon. Divide the total binding energy by the number of nucleons (238) to find \( \text{Binding energy per nucleon} = \frac{\text{Binding energy}}{238} \).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Mass Defect

The mass defect is the difference between the mass of an atomic nucleus and the sum of the masses of its individual protons and neutrons. This discrepancy arises because some mass is converted into energy when nucleons bind together, according to Einstein's equation E=mc². Understanding mass defect is crucial for calculating the binding energy of a nucleus.
추천 영상:
가이드 코스
20:32
Mass Spectrometers

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is a measure of the stability of a nucleus; a higher binding energy indicates a more stable nucleus. The binding energy can be calculated using the mass defect and is often expressed in mega-electronvolts (MeV).
추천 영상:
가이드 코스
04:10
Intro to Energy & Types of Energy

Binding Energy per Nucleon

Binding energy per nucleon is the binding energy divided by the total number of nucleons (protons and neutrons) in the nucleus. This value provides insight into the stability of the nucleus relative to its size, allowing for comparisons between different isotopes. A higher binding energy per nucleon generally indicates a more stable nucleus.
추천 영상:
가이드 코스
04:10
Intro to Energy & Types of Energy
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