Question

To calculate avogadro's number from the measured density of copper shot, what additional information is not needed? the molar mass of copper the atomic number of copper the length of the edge of the unit cell of copper the number of copper atoms occupying one unit cell of copper

Answer 1

Answer is Atomic Number of Cu.

Step-by-step explanation: For a unit cell, density can be written as

`Density=\frac{\text{mass of unit cell}}{\text{volume of unit cell}}`

For a unit cell, Mass will be

`\text{Mass of unit cell}=Z* m`

where Z= Number of atoms

m = Mass of an atom

Mass of an atom can be calculated by,

`m=\frac{\text{Molar Mass}}{\text{Avagadro's Number}}\\m=(M)/(N_A)`

Volume of a unit cell =
`\text{edge length}^3`

`Volume=(a)^3`

where a = edge length

Now, putting Mass and Volume of an atom in density, the equation becomes

`\rho=(Z* M)/(a^3* N_A)`

For the calculation of Avagadro's number,

`N_A=(Z* M)/(a^3* \rho)`

we can see from the equation, we need

1. Molar mass of atom

2. Density of unit cell

3. Edge length of the unit cell

4. Number of atoms occupying one unit cell.

Hence, for the above question there is no need for the Atomic Number of atom.