The RAM of copper is 63.5g\mol and its density is 8.93×10^3kgm^3.in each cubic metre of the metal,there are 8.24×10^28free electrons. Calculate the number of free electrons contributed per atom
1m^3/8.93*10^3kg * .0635kg/mol * 6.023*10^23atoms/mol = 4.2829*10^18 atoms
wow -- roughly 10^10 electrons per atom?
I don't think so. I suspect a typo.
Number of atoms per cubic meter =
(Mass per cubic meter/MM)*Avagadro's No.
= (8.93*10^3/63.5*10^-3)*6.022*10^23
= 8.4*10^28
Hence, the number of atoms in free electrons in each cubic meter are almost the same, and the answer is one.
To calculate the number of free electrons contributed per atom, we need to find the number of atoms present in one cubic meter of copper and then divide it by the number of free electrons.
Here's how we can do that:
1. Start with the density of copper, which is given as 8.93 × 10^3 kg/m^3. This means that in one cubic meter of copper, we have a mass of 8.93 × 10^3 kg.
2. Convert the mass of copper to the number of moles. We can use the molar mass of copper, which is given as 63.5 g/mol. Since 1 mole = 6.022 × 10^23 atoms, we can calculate the number of moles using the formula:
Moles of copper = (mass of copper)/(molar mass of copper)
Moles of copper = (8.93 × 10^3 kg) / (63.5 g/mol)
3. Calculate the number of atoms in one cubic meter of copper by multiplying the moles of copper by Avogadro's number:
Number of atoms = (moles of copper) × (Avogadro's number)
4. Now that we have the number of atoms, we can calculate the number of free electrons per atom by dividing the given number of free electrons by the number of atoms:
Number of free electrons per atom = (number of free electrons) / (number of atoms)
Substituting the given values:
Number of free electrons per atom = (8.24 × 10^28 electrons) / (number of atoms)
This calculation will give us the number of free electrons contributed per atom in copper.