Domanda del libro di testo
A sample of 1.0 x 1010 atoms that decay by alpha emission has a half-life of 100 min. How many alpha particles are emitted between t = 50 min and t = 200 min?
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Ch 42: Nuclear Physics
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 42, Problema 15
Use the potential-energy diagram in Figure 42.8 to estimate the ratio of the gravitational potential energy to the nuclear potential energy for two neutrons separated by 1.0 fm.
Guida verificata passo dopo passo1
Identify the key quantities from the problem: gravitational potential energy and nuclear potential energy. Gravitational potential energy is given by the formula: , where is the gravitational constant, is the mass of a neutron, and is the separation distance. Nuclear potential energy can be estimated from the potential-energy diagram provided in the problem.
From the potential-energy diagram (Figure 42.8), determine the nuclear potential energy at a separation distance of 1.0 fm (1.0 × 10-15 m). This value is typically negative and represents the attractive nuclear force between the neutrons.
Calculate the gravitational potential energy using the formula: . Substitute the known values: , , and . This will yield the gravitational potential energy between the two neutrons.
Determine the ratio of gravitational potential energy to nuclear potential energy. This is done by dividing the magnitude of the gravitational potential energy by the magnitude of the nuclear potential energy: .
Interpret the result. The ratio will likely show that the nuclear potential energy is significantly stronger than the gravitational potential energy at this separation distance, reflecting the dominance of nuclear forces at subatomic scales.
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Concetti chiave
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Gravitational Potential Energy
Gravitational potential energy (U_g) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula U_g = -G(m1*m2)/r, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers. In the context of neutrons, this energy is relatively small compared to nuclear forces at short distances.
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Percorso guidato
06:35
Gravitational Potential Energy
Nuclear Potential Energy
Nuclear potential energy (U_n) refers to the energy associated with the interactions between nucleons (protons and neutrons) within an atomic nucleus. This energy is significantly stronger than gravitational potential energy at very short ranges, typically on the order of femtometers (fm). The nuclear force is attractive at these distances, leading to a negative potential energy value that reflects the stability of the nucleus.
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07:24Potential Energy Graphs
Potential Energy Ratio
The potential energy ratio compares the magnitudes of gravitational potential energy to nuclear potential energy. This ratio is crucial for understanding the relative strengths of these forces acting on particles like neutrons. By estimating this ratio, one can infer the dominance of nuclear forces over gravitational forces at small scales, which is essential in nuclear physics and astrophysics.
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Percorso guidato
07:24Potential Energy Graphs
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