   Chapter 2, Problem 153GQ

Chapter
Section
Textbook Problem

Consider an atom of 64Zn.(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)

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.

Explanation

The radius of the zinc nucleus is given that 4.8×106nm=4.8×1013cm.

Equation for finding Volume of sphere is,

Volume=(4/3)πr3

Therefore, the volume of zinc nucleus is,

Volume=(4/3)3.14×(4.8×1013cm)3 =463.01×1039cm3

Mass of the zinc atom is 1

(b)

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

(c)

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

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