Calculate the mobile electron density for nickel. A mole of...

Calculate the mobile electron density for nickel. A mole of nickel has a mass of $59 \mathrm{g}(0.059 \mathrm{kg})$, and one mobile electron is released by each atom in metallic nickel. The density of nickel is about $8.8 \mathrm{g} / \mathrm{cm}^{3},$ or $8.8 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$.

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole or kilograms per mole. It provides the conversion between the mass of a material and the number of moles, which is crucial when calculating the number of atoms or particles present in a given mass of a material.

Avogadro's Number

Avogadro's number is a fundamental constant that represents the number of constituent particles, usually atoms or molecules, in one mole of a substance. This constant allows the conversion from the number of moles to the total number of atoms, which is essential in calculations involving particle counts such as the mobile electron density in metals.

Density

Density is defined as mass per unit volume, and it plays a critical role in relating the macroscopic mass of a material to its microscopic properties. In problems involving conduction electrons in metals, density is used to connect the material's mass to its volume, enabling the determination of how many atoms (and therefore electrons) exist per unit volume.

Mobile Electron Density in Metals

Mobile electron density refers to the number of conduction electrons present per unit volume in a metal. In the context of metallic conduction, it is assumed that these electrons, which are loosely bound to atoms, are free to move and contribute to electrical conductivity. Calculating this density involves determining the number of conduction electrons (using mole-to-atom conversions) and dividing by the volume determined from the metal's density.

Transcript

00:01 Okay, so this is the question test our understanding on the crystal unit cell.

00:08 In order to solve this question, you have to have an analogy that relates the microscopic unit cell to the macroscopic properties of the material, such as the density.

00:24 So let's summarize the information the question gives.

00:27 It first says a nickel has a phase -centered unit cell, phase -centered cubic unicell, and it's nickel.

00:44 And also, it gives you the edge length, which is 352 .4 picometers.

00:54 And usually, it's better to first convert them into meters, so it's actually equals to 352 .52 times 102 .2.

01:04 To minus 12 meters.

01:09 And another piece of information that gives is the density of the macroscopic nickel metal is 8 .91 grams per centimeter cube.

01:25 And same, we need to convert into meters.

01:29 So it's equal to 8 .91 times 10 to 6 grams per centimeter cubes.

01:40 And what i ask is the mass of the nickel atoms and also calculate the f -gallon number.

01:52 So in order to solve this question, the first step when to do is to calculate the mass of the single unit cell.

02:12 So we know the mass of single unit cell is equal to the density times the volume of the cell.

02:23 The density is already given here is actually 8 .91 times 10 to 6.

02:36 And the volume of cell actually equals to the length of the cell power 3.

02:48 And now this is actually equals to 3 .899.

02:55 X .9 .3 times 10 to 8 times 10 to 6 times 10 to minus 36.

03:11 And this equals to 3 .893 times 10 to minus 22 grams...

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