Calc Lattice Constant of Solid Manganese

[adambinch]

I am told solid manganese exists in a simple cubic structure. If its Ar is 54.94 and its density is 7440 Kg m^-3, How do I calculate the lattice constant for this material?

 

[Mapes]

Hi adambinch, welcome to PF. You need to find out how many atoms there are in the simple cubic unit cell. Then you can set up a calculation like

$$\left(\frac{\mathrm{atoms}}{\mathrm{cell}}\right)\left(\frac{\mathrm{weight}}{\mathrm{mole}}\right)\left(\frac{\mathrm{mole}}{\mathrm{atoms}}\right)\left(\frac{\mathrm{volume}}{\mathrm{weight}}\right)=\left(\frac{\mathrm{volume}}{\mathrm{cell}}\right)$$

and the volume per unit cell should lead you to the lattice parameter. Does this help?

 

[charng]

To calculate the lattice constant of solid manganese, we can use the formula a = (4M/ρ)^1/3, where a is the lattice constant, M is the molar mass of manganese (54.94 g/mol), and ρ is the density of solid manganese (7440 kg/m^3). Plugging in the values, we get a = (4*54.94 g/mol / 7440 kg/m^3)^1/3 = 0.325 nm. This means that the lattice constant for solid manganese is 0.325 nanometers. This value is important as it represents the distance between the atoms in the simple cubic structure of solid manganese.