How to Calculate and Solve for Normally Occupied Positions | Ceramics

Last Updated on March 30, 2024

The image above represents normally occupied positions in ceramics. To calculate normally occupied positions, four essential parameters are needed, and these parameters are Avogadro’s number (N_A), Density (ρ), Atomic weight (A_K) and Atomic weights (A_G).

The Formula for Calculating Normally Occupied Positions

N = ^N_Aρ / _{(AK + AG)}

N = Normally Occupied Positions
N_A = Avogadro’s Number
A_K, A_G = Atomic Weights
ρ = Density

Let’s solve the following example below:
Find the normally occupied positions when the avogadro’s number is 6.022e+23, atomic weight is 12, atomic weight is 16 and the density is 10.

This implies the following;

N_A = Avogadro’s Number = 6.022e+23
A_K, A_G = Atomic Weights = 12, 16
ρ = Density = 10

N = ^N_Aρ / _{(AK + AG)}
So, N = ^{(6.022e+23)(10)}/_{(12 + 16)}
N = ^(6.022e+24)/₍₂₈₎
N = 2.15e+23

Therefore, the normally occupied positions is 2.15e+23.

Calculating the Density when the Normally Occupied Positions, the Avogadro’s Number, the Atomic Weights are Given

ρ = ^{N (A_K + A_G)} / _NA

Where;

ρ = Density
N = Normally Occupied Positions
N_A = Avogadro’s Number
A_K, A_G = Atomic Weights

Let’s solve the following example below:
Given that normally occupied positions is 20, the avogadro’s number is 6.022e+23, atomic weights is 18, 6.

This implies the following:

N = Normally Occupied Positions =20
N_A = Avogadro’s Number = 6.022e+23
A_K, A_G = Atomic Weights = 18, 6

ρ = ^{N (A_K + A_G)} / _NA
ρ = ^{20 (18 + 6)} / _6.022e+23
Then, ρ = ^{20 (24)} / _6.022e+23
ρ = ⁴⁸⁰ / _6.022e+23
ρ = 7.970e-22

Therefore, the density is 7.970e-22.

Calculating the Atomic Weight (A_K) when the Normally Occupied Positions, the Avogadro’s Number, Density and Atomic Weight (A_G) are Given

A_K = ^N_Aρ / _N – A_G

Where;

ρ = Density
N = Normally Occupied Positions
N_A = Avogadro’s Number
A_K, A_G = Atomic Weights

Let’s solve the following example below:
Find the atomic weight when the normally occupied positions is 24, the density is 12, the avogadro’s number is 6.022e+23 and the atomic weight is 10.

This implies the following:

ρ = Density = 12
N = Normally Occupied Positions = 24
N_A = Avogadro’s Number = 6.022e+23
A_G = Atomic Weights = 10

Then, A_K = ^N_Aρ / _N – A_G
A_K = ^{6.022e+23 x 12} / ₂₄ – 10
That is, A_K = ^7.2264e+24 / ₂₄ – 10
A_K = 3.011e-23 – 10
A_K = – 6.98e-23

Therefore, the atomic weight is – 6.98e-23.

Read more: How to Calculate and Solve for Flexural Strength for Rectangular Cross-section in Defects | Ceramics

Calculating the Atomic Weight (A_G) when the Normally Occupied Positions, the Avogadro’s Number, Density and Atomic Weight (A_K) are Given

A_G = ^N_Aρ / _N – A_K

Where;

ρ = Density
N = Normally Occupied Positions
N_A = Avogadro’s Number
A_K, A_G = Atomic Weights

Let’s solve for the following example:
Find the atomic weight when the normally occupied positions is 10, the density is 10, the avogadro’s number is 6.022e+23 and the atomic weight is 4.

This implies the following:

ρ = Density = 10
N = Normally Occupied Positions = 10
N_A = Avogadro’s Number = 6.022e+23
A_G = Atomic Weights = 4

So, A_G = ^N_Aρ / _N – A_K
A_G = ^{6.022e+23 x 10} / ₁₀ – 4
That is, A_G = ^6.022e+24 / ₁₀ – 4
A_G = 6.022e-23 – 4
A_G = 2.022e-23

Therefore, the atomic weight is 2.022e-23.

Read more: How to Calculate and Solve for Theoretical Density of Ceramics | Ceramics

How to Calculate and Solve for Normally Occupied Positions in Ceramics Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the normally occupied positions.

To get the answer and workings of the normally occupied positions using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials & Metallurgical under Engineering.

So, Click on Ceramics under Material & Metallurgical

Then, Click on Normally Occupied Positions under Ceramics

So, the screenshot below displays the page or activity to enter your values, to get the answer for the normally occupied positions according to the respective parameters which are the Avogadro’s number (N_A), Density (ρ), Atomic weight (A_K) and Atomic weights (A_G).

Then, enter the values appropriately and accordingly for the parameters as required by the Avogadro’s number (N_A) is 6.022e+23, Density (ρ) is 10, Atomic weight (A_K) is 12 and Atomic weights (A_G) is 16.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the normally occupied positions and presents the formula, workings and steps too.