Open Question
What is the radius (in cm) of a pure copper sphere that contains 1.14 * 10^24 copper atoms? [The volume of a sphere is (4/3)πr^3 and the density of copper is 8.96 g/cm^3.]
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1. Intro to General Chemistry
Density of Geometric Objects
Multiple Choice
Chromium crystallizes in a body-centered cubic structure with an atomic radius of 125 pm. Given that the atomic mass of chromium is 51.9961 g/mol, estimate the density of Cr metal in g/cm³.
A
8.04 g/cm³
B
7.19 g/cm³
C
6.25 g/cm³
D
5.32 g/cm³
Verified step by step guidance1
Identify the type of crystal structure: Chromium crystallizes in a body-centered cubic (BCC) structure.
Calculate the volume of the unit cell: In a BCC structure, the relationship between the atomic radius (r) and the edge length (a) of the cube is given by \( a = \frac{4r}{\sqrt{3}} \). Substitute the atomic radius of chromium (125 pm) into this formula to find the edge length in picometers.
Convert the edge length from picometers to centimeters: Since 1 pm = 1e-12 m and 1 m = 100 cm, convert the edge length from pm to cm.
Determine the mass of atoms in the unit cell: In a BCC structure, there are 2 atoms per unit cell. Use the atomic mass of chromium (51.9961 g/mol) and Avogadro's number (6.022e23 atoms/mol) to calculate the mass of 2 atoms in grams.
Calculate the density: Density is mass divided by volume. Use the mass of the unit cell (from step 4) and the volume of the unit cell (from step 3) to calculate the density of chromium in g/cm³.
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