1) Mass of one copper atom: ![1.063\cdot 10^{-22} kg](https://tex.z-dn.net/?f=1.063%5Ccdot%2010%5E%7B-22%7D%20kg)
2) There are
atoms in the cube
3) Mass of the cubical block: 992 kg
Explanation:
1)
We are told here that the mass of one mole of copper is
![M=64 g](https://tex.z-dn.net/?f=M%3D64%20g)
for
(number of moles)
We also know that the number of atoms inside 1 mole of substance is equal to Avogadro number:
![N_A = 6.022\cdot 10^{23}](https://tex.z-dn.net/?f=N_A%20%3D%206.022%5Ccdot%2010%5E%7B23%7D)
This means that
atoms of copper have a mass of M = 64 g. Therefore, we can find the mass of one copper atom by dividing the total mass by the avogadro number:
![m=\frac{M}{N_A}=\frac{64}{6.022\cdot 10^{23}}=1.063\cdot 10^{-22} kg](https://tex.z-dn.net/?f=m%3D%5Cfrac%7BM%7D%7BN_A%7D%3D%5Cfrac%7B64%7D%7B6.022%5Ccdot%2010%5E%7B23%7D%7D%3D1.063%5Ccdot%2010%5E%7B-22%7D%20kg)
2)
We are told that the diameter of a copper atom is
![d=2.28\cdot 10^{-10} m](https://tex.z-dn.net/?f=d%3D2.28%5Ccdot%2010%5E%7B-10%7D%20m)
We can assume that the atoms are arranged in a cube, and that they are all attached to each other; so the side of the cube can be written as size of one atom multiplied by the number of atom per side:
![L=Nd](https://tex.z-dn.net/?f=L%3DNd)
where
N is the number of atoms (rows) in one side of the cube
Since the side of the cube is
L = 4.8 cm = 0.048 m
We find N:
![N=\frac{L}{d}=\frac{0.048}{2.28\cdot 10^{-10}}=2.11\cdot 10^8](https://tex.z-dn.net/?f=N%3D%5Cfrac%7BL%7D%7Bd%7D%3D%5Cfrac%7B0.048%7D%7B2.28%5Ccdot%2010%5E%7B-10%7D%7D%3D2.11%5Ccdot%2010%5E8)
This is the number of atom rows per side; therefore, the total number of atoms in the cube is
![N^3=(2.11\cdot 10^8)^3=9.33\cdot 10^{24}](https://tex.z-dn.net/?f=N%5E3%3D%282.11%5Ccdot%2010%5E8%29%5E3%3D9.33%5Ccdot%2010%5E%7B24%7D)
3)
The total mass of the cubical block of copper will be given by the mass of one atom of copper multiplied by the total number of atoms, so:
![M= N^3 m](https://tex.z-dn.net/?f=M%3D%20N%5E3%20m)
where:
is the number of atoms in the cube
is the mass of one atom
Therefore, substituting, we find:
![M=(9.33\cdot 10^{24})(1.063\cdot 10^{-22})=992 kg](https://tex.z-dn.net/?f=M%3D%289.33%5Ccdot%2010%5E%7B24%7D%29%281.063%5Ccdot%2010%5E%7B-22%7D%29%3D992%20kg)
So, the mass of the cubical block is 992 kg.
Learn more about mass and density:
brainly.com/question/5055270
brainly.com/question/8441651
#LearnwithBrainly