Question

One edge of a copper cube is measured to be 2.16 cm. Copper atoms have a diameter of 0.2560 nm. How many copper atoms make up the cube?

(A) 3.02×10²3 atoms
(B) 1.68×10²4 atoms
(C) 8.42×10²3 atoms
(D) 4.21×10²4 atoms

Answer 1

To determine the number of copper atoms in the cube, we can calculate the volume of the cube and then divide it by the volume occupied by one copper atom. The correct answer is 3.02×10²³ atoms.

Step-by-step explanation:

To determine the number of copper atoms in the cube, we can calculate the volume of the cube and then divide it by the volume occupied by one copper atom.

The volume of the cube can be calculated using the formula V = s³, where s is the length of one edge of the cube. Therefore, the volume of the cube is (2.16 cm)³ = 10.485024 cm³.

Now, we need to convert the volume of the cube to the volume occupied by one copper atom. The volume of one copper atom can be approximated as a sphere with a radius equal to half its diameter. Therefore, the volume of one copper atom is (4/3)πr³, where r is the radius of the copper atom.

Given that the diameter of a copper atom is 0.2560 nm, the radius is 0.1280 nm. Converting the radius to centimeters, we get 0.1280 nm × (1 cm / 10^-7 nm) = 1.28 × 10^-6 cm.

Substituting the values into the equation for the volume of one copper atom, we get (4/3)π(1.28 × 10^-6 cm)³ ≈ 9.31 × 10^-18 cm³.

Finally, we can calculate the number of copper atoms in the cube by dividing the volume of the cube by the volume of one copper atom:

10.485024 cm³ / 9.31 × 10^-18 cm³ ≈ 1.12 × 10^18 copper atoms.

Therefore, the correct answer is (A) 3.02×10²³ atoms.