MHTCET 14 May 2023 Shift 2 Solved Paper

The density ( ρ ) of a simple cubic unit cell is calculated using:
ρ=‌

Z⋅M

a3⋅NA

Where:
Z= Number of atoms per unit cell (1 for simple cubic)
M= Molar mass of the metal (g∕mol)
a= Edge length of the unit cell (cm )
NA= Avogadro's Number (6.022×1023mol−1)
Finding the Edge Length (a):
‌a3=‌

21.5cm3mol−1

NA

‌a3=‌

21.5cm3mol−1

6.022×1023mol−1

‌a3=3.57×10−23cm3
‌a=3.29×10−8‌cm
Calculating Density (ρ) :
‌ρ=9.77gcm−3
Answer:
The density of the metal is 9.77g∕cm3.