**Title: Calculating Atoms in a Unit Cell****Question:**Calculate the total number of atoms contained within this unit cell.**Diagram:**The diagram shows a cubic unit cell structure with atoms represented by circles. The vertices of the cube and the centers of the cube faces are occupied by atoms. This configuration typically represents a face-centered cubic (FCC) lattice.**Answer Choices:**A) 8 atoms B) 4 atoms C) 2 atoms D) 1 atom **Explanation:**In a face-centered cubic (FCC) lattice:- Each corner atom is shared by 8 adjacent unit cells.- Each face-centered atom is shared by 2 adjacent unit cells.- There are 8 corner atoms (each contributing 1/8th of an atom) and 6 face-centered atoms (each contributing 1/2 of an atom).To calculate the total number of atoms in one FCC unit cell:- Contributions from corner atoms: \(8 \times \frac{1}{8} = 1\) atom- Contributions from face-centered atoms: \(6 \times \frac{1}{2} = 3\) atoms- Total number of atoms: \(1 + 3 = 4\) atomsThus, the correct answer is **B) 4 atoms**.

The unit cell is defined as the repeating unit of the crystal lattice. It is the building block of a crystal.The given unit cell is a simple cubic cell. In a given simple cubic cell, 8 atoms are present in the corner of the cubic cell. To find out the total no. of atoms in a simple cubic cell, we need to use the formulaThere are a total of 8 atoms present on the corner of the cubic cell. Hence, the total no. of atoms in a cell isTherefore, the total no. of atoms contained within a unit cell is 1 atom. Hence, "option D" is correct.All other options do not match the calculated value. Hence, options A, B, and C are incorrect, as a simple cubic unit cell contains only 1 atom.The total number of atoms present in a unit cell is 1 atom. Hence, "option D" is correct.

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Calculate the total number of atoms contained within this unit cell. --O A) 8 atoms B) 4 atoms C) 2 atoms D) 1 atom

Chemistry

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ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

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Crystal Lattices and Unit Cell

Consider a crystal. The regular and repeating pattern of constituent particles is the most distinguishing feature of crystalline solids. A crystal lattice is formed when these particles are replaced with representative points. The three-dimensional arrangement of constituent particles is known as a crystal lattice. Unit cell is that the smallest portion of a space lattice which when repeated in several directions, generate the whole lattice. Unit cell is a building block of a lattice. It is the smallest unit of cell.

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