Answer:
3.37 cm
Step-by-step:
The edge length of the titanium cube can be calculated using the formula:
Edge length = (Volume of cube)^(1/3)
And the volume of the cube can be calculated as follows:
1. Calculate the mass of the titanium atoms in the cube.
The mass of one titanium atom can be calculated by dividing the molar mass of titanium by Avogadro's number:
Mass of one titanium atom = Molar mass of titanium / Avogadro's number
= 47.867 g/mol / (6.022 × 10^23 atoms/mol)
= 7.943 × 10^-23 g/atom
The total mass of the titanium atoms in the cube is then:
Total mass of titanium atoms = (2.23 × 10^24 atoms) × (7.943 × 10^-23 g/atom)
= 1.773 × 10^2 g
2. Calculate the volume of the titanium cube.
The volume of the cube can be calculated by dividing the total mass of the titanium atoms by the density of titanium:
Volume of cube = Total mass of titanium atoms / Density of titanium
= 1.773 × 10^2 g / 4.50 g/cm^3
= 39.4 cm^3
3. Calculate the edge length of the titanium cube.
Finally, the edge length of the cube can be calculated as:
Edge length = (Volume of cube)^(1/3)
= (39.4 cm^3)^(1/3)
= 3.37 cm
So the edge length of the titanium cube is 3.37 cm, rounded to three significant figures.
Hope this helps!