Consider an atom of 64 Zn. (a) Calculate the density of the nucleus in grams per cubic centimeter, knowing that the nuclear radius is 4.8 × 10 –6 nm and the mass of the 64 Zn atom is 1.06 × 10 –22 g. (Recall that the volume of a sphere is [4/3] πτ 3 .) (b) Calculate the density of the space occupied by the electrons in the zinc atom, given that the atomic radius is 0.125 nm and the electron mass is 9.11 × 10 –28 g. (c) Having calculated these densities, what statement can you make about the relative densities of the parts of the atom?
Consider an atom of 64 Zn. (a) Calculate the density of the nucleus in grams per cubic centimeter, knowing that the nuclear radius is 4.8 × 10 –6 nm and the mass of the 64 Zn atom is 1.06 × 10 –22 g. (Recall that the volume of a sphere is [4/3] πτ 3 .) (b) Calculate the density of the space occupied by the electrons in the zinc atom, given that the atomic radius is 0.125 nm and the electron mass is 9.11 × 10 –28 g. (c) Having calculated these densities, what statement can you make about the relative densities of the parts of the atom?
(a) Calculate the density of the nucleus in grams per cubic centimeter, knowing that the nuclear radius is 4.8 × 10–6 nm and the mass of the 64Zn atom is 1.06 × 10–22 g. (Recall that the volume of a sphere is [4/3] πτ3.)
(b) Calculate the density of the space occupied by the electrons in the zinc atom, given that the atomic radius is 0.125 nm and the electron mass is 9.11 × 10–28 g.
(c) Having calculated these densities, what statement can you make about the relative densities of the parts of the atom?
(a)
Expert Solution
Interpretation Introduction
Interpretation: For given atom of 64Zn, the density of nucleus in grams should be calculated in per cubic centimeter using the given nuclear radium and the mass of the atom.
Concept introduction:
Equation for density from volume and mass is,
Density=MassVolume
Equation for finding Volume of sphere is,
Volume=(4/3)πr3
Mass: It is the quantitative measure of a substance. The amount of matter present in substance is expressed as mass. The S.I. unit of mass is kg.
Answer to Problem 153GQ
The density of zinc nucleus is 2.3×1014g/cm3
Explanation of Solution
The radius of the zinc nucleus is given that 4.8×10−6nm=4.8×10−13cm.
Equation for finding Volume of sphere is,
Volume=(4/3)πr3
Therefore, the volume of zinc nucleus is,
Volume=(4/3)3.14×(4.8×10−13cm)3=463.01×10−39cm3
Mass of the zinc atom is 1.06×10−22g
Equation for density from volume and mass is,
Density=MassVolume
Therefore, the density of zinc nucleus is,
Density=1.06×10−22g463.01×10−39cm3=2.3×1014g/cm3
(b)
Expert Solution
Interpretation Introduction
Interpretation: For given atom of 64Zn, the density of space occupied by electrons in atom with atomic radius and the mass of electron should be calculated.
Concept introduction:
Equation for density from volume and mass is,
Density=MassVolume
Equation for finding Volume of sphere is,
Volume=(4/3)πr3
Answer to Problem 153GQ
The density of space occupied by electrons in Zn atom is 3.34×10−3g/cm3
Explanation of Solution
The radius of the zinc atom is given that 0.125nm=1.25×10−8cm.
Equation for finding Volume of sphere is,
Volume=(4/3)πr3
Therefore, the volume of zinc nucleus is,
Volume=(4/3)3.14×(1.25×10−8cm)3=8.17×10−24cm3
The volume of zinc nucleus is 463.01×10−39cm3, which negligibly small quantity, so the volume occupied by electrons in Zn atom is approximately equals to the volume of atom,
Volume=8.17×10−24cm3
Mass of the zinc atom is the sum of mass of nucleus and mass of total number of electrons, that is 30×9.11×10−28g=2.73×10−26g
Equation for density from volume and mass is,
Density=MassVolume
Therefore, the density of space occupied by electrons in Zn atom is,
Density=2.73×10−26g8.17×10−24cm3=3.34×10−3g/cm3
(c)
Expert Solution
Interpretation Introduction
Interpretation: Considering the density of nucleus and the density of space occupied by electrons in given atoms the statement that describes about relative densities of parts of given atom should be identified.
Concept introduction:
Equation for density from volume and mass is,
Density=MassVolume
Equation for finding Volume of sphere is,
Volume=(4/3)πr3
Answer to Problem 153GQ
The density of nucleus is far greater than the density of space occupied by electrons (outside nucleus in atom).
Explanation of Solution
The density of zinc nucleus is found that 2.3×1014g/cm3
The density of space occupied by electrons in Zn atom is found that 3.34×10−3g/cm3.
The ratio of density of zinc nucleus to density of space occupied by electrons is,
2.3×1014g/cm33.34×10−3g/cm3=688.6
Hence, the density of nucleus is far greater than the density of space occupied by electrons (outside nucleus in atom).
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(a) Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 8.0 g. Silver has 47 electrons per atom, and its molar mass is 107.87 g/mol.
(b) Imagine adding electrons to the pin until the negative charge has the very large value 2.00 mC. How many electrons are added for every 109 electrons already present?
(a) Atoms are very small compared to objects on the macroscopic scale. The radius of a vanadium atom is 131 pm. What is this value in meters and in
centimeters?
cm
(b) The mass of a single vanadium atom is 8.46×10-23 g. Suppose enough V atoms were lined up like beads on a string to span a distance of 44.7 cm ( 18
atoms
inches). How many atoms would be required?
What mass in grams of V would be used?
Could you weigh out this amount of vanadium using a typical laboratory balance?
(c) Taking the density of vanadium metal to be 6.08 g/cm³, calculate the mass of metal needed to form a piece of V wire with the same length as the
distance in b, but with a diameter of 1.00 mm. Hint: The volume of a cylinder is T times its radius squared times its height. (V = T r² h)
How many vanadium atoms does this represent?
atoms
Helium is the lightest noble gas and the second most abundant element (after hydrogen) in the universe.
(a) The radius of a helium atom is 3.1x10-11 m; the radius of its nucleus is 2.5x10-15 m. What fraction of the spherical atomic volume is occupied by the nucleus (V of a sphere 5 4/ 3πr3)?
(b) The mass of a helium-4 atom is 6.64648x10-24 g, and each of its two electrons has a mass of 9.10939x10-28 g.
What fraction of this atom’s mass is contributed by its nucleus?
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Atomic Number, Atomic Mass, and the Atomic Structure | How to Pass ChemistryThe Nucleus: Crash Course Chemistry #1; Author: Crash Course;https://www.youtube.com/watch?v=FSyAehMdpyI;License: Standard YouTube License, CC-BY