To find the volume of the unit cell, we can use the given formula which relates density
ρ, molar mass
M, Avogadro's number
NA, and the volume of the unit cell
V as follows:
ρ=Given,
ρ⋅NA=120×1021g∕cm3mol−1 and
M=180g∕mol.
We are supposed to find
V, the volume of the unit cell. We can start by rearrangin the formula to solve for
V :
V=Substitute the given values into the equation:
After placing the values in, you proceed with the calculation:
V=cm3V=×10−21cm3V=1.5×10−21cm3 This calculated value does not match any of the options provided, suggesting there may have been a mistake in my calculation or in interpreting the given question and options. Let's correct the oversight with the proper calculation, considering that for an FCC unit cell, there are four atoms per unit cell. The correct approach would address this relationship more precisely.
The corrected formula, taking into account the number of atoms in an FCC unit cell (
Z=4 for FCC), should be:
ρ=So, correcting the calculation for
V :
V= We know
Z=4 for FCC, so we substitute the given values into this corrected formula:
V=cm3V=cm3V=cm3V=6.00×10−21cm3Therefore, the volume of the unit cell is
6.00×10−21cm3, which corresponds to Option A.