Chapter 3, Problem 3.104CP

Interpretation Introduction

Interpretation:

The program to calculate packing fraction and theoretical density for an element in a cubic structure needs to be determined.

Concept introduction:

Computer programs are made to simplify any calculation. They are designed in such a way that after entring the input, with one click output can be obtained. It can solve long calculations in fraction of seconds.

Also, it provides the accurate solution to the problem.

In the given program, input is atomic mass, atomic radius and cubic structure of an element and output is packing fraction and theoretical density of the element.

The packing fraction and theoretical density of the element can be calculated mannualy from the following formulas:

Packing fraction =

  $\frac{4\times 22\times \text{Number of atom per cell}\times {\left(\text{atomic radius}\right)}^3}{3\times 7\times {\left(\text{lattice parameter}\right)}^3}$

Theoretical density =

  $\frac{\text{Number of atom per cell×atomic mass}}{\text{6}{\text{.022×10}}^{\text{23}}\text{×}{\left(\text{lattice parameter}\right)}^{\text{3}}}$