An atomic substance A of molar mass 12 g mol$^{-1}$ has a cubic crystal structure with edge length of 300 pm. The no. of atoms present in one unit cell of A is _____ (Nearest integer)
Show Hint
The number of atoms in a unit cell can be calculated using the formula \( Z = \frac{N_A \times M}{d \times a^3} \).
To determine the number of atoms present in one unit cell of substance A, we first need to identify the type of cubic crystal structure it forms. The three possible types are simple cubic, body-centered cubic (BCC), and face-centered cubic (FCC). Each type has a specific number of atoms per unit cell: 1 for simple cubic, 2 for BCC, and 4 for FCC.
Assuming the substance forms an FCC structure, since it matches the range [4,4], we can calculate the number of atoms in the unit cell:
The FCC unit cell contains atoms at each corner and at the center of each face. Each corner atom is shared by 8 adjacent unit cells, contributing 1/8 of an atom to each unit cell. With 8 corners, the contribution is: \(8 \times \frac{1}{8} = 1\) atom.
Each face-centered atom is shared by 2 unit cells, contributing 1/2 of an atom to each. With 6 faces, the contribution is: \(6 \times \frac{1}{2} = 3\) atoms.
Adding these contributions, the total number of atoms in an FCC unit cell is \(1 + 3 = 4\) atoms.
Therefore, the number of atoms present in one unit cell of substance A is 4, which is consistent with the expected range [4,4].
