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Ch 37: The Foundations of Modern Physics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 37: The Foundations of Modern PhysicsProblema 23b
Capitolo 37, Problema 23b

Consider the gold isotope 197Au. The gold nucleus has a diameter of 14.0 fm. What is the density of matter in a gold nucleus?

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1
Determine the volume of the gold nucleus, assuming it is spherical. The formula for the volume of a sphere is: V=43πr3, where r is the radius of the nucleus. The radius is half the diameter, so r=14.02 fm.
Convert the radius from femtometers (fm) to meters, as the SI unit for density is kg/m³. Use the conversion factor: 1 fm=1×10-15 m.
Calculate the mass of the gold nucleus. The mass of the nucleus is approximately equal to the mass of its nucleons (protons and neutrons). For gold-197, the mass is approximately 197 u, where u is the atomic mass unit. Convert this to kilograms using the conversion factor: 1 u=1.66×10-27 kg.
Calculate the density of the gold nucleus using the formula: ρ=mV, where m is the mass of the nucleus and V is its volume.
Substitute the values for mass and volume into the density formula, ensuring all units are consistent (mass in kilograms and volume in cubic meters). Simplify the expression to find the density of matter in the gold nucleus.

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Nuclear Density

Nuclear density refers to the mass per unit volume of a nucleus. It is typically expressed in units of kilograms per cubic meter (kg/m³) and is remarkably high due to the compact arrangement of nucleons (protons and neutrons) within the nucleus. For most atomic nuclei, the density is approximately 2.3 x 10^17 kg/m³, which is significantly greater than the density of ordinary matter.
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Intro to Density

Volume of a Sphere

The volume of a sphere is calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. In the context of a nucleus, this formula allows us to determine the volume based on its diameter. Understanding how to calculate the volume is essential for determining the density of the nucleus, as density is defined as mass divided by volume.
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Volume Thermal Expansion

Isotopes and Atomic Mass

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For example, the gold isotope 197Au has 79 protons and 118 neutrons. The atomic mass of an isotope is crucial for calculating the total mass of the nucleus, which is necessary for determining its density.
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Charge of Atom
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