If we wanted a block of iron of mass 3.25 kg to acquire a positive charge of 0.100 C, what fraction of the electrons would we have to remove?
To determine the fraction of electrons that would need to be removed to give the block of iron a positive charge of 0.100 C, we need to calculate the number of electrons in the block and the charge of a single electron.
1. Calculate the number of electrons in the block of iron:
To find the number of electrons in the block, we need to know the mass of the iron block and the molar mass of iron (Fe).
The molar mass of Fe is approximately 55.85 g/mol, which is equal to 0.05585 kg/mol since 1 mole = 6.022 × 10^23 particles (Avogadro's number).
To find the number of moles of iron in the block, we divide the mass of the block by the molar mass:
Number of moles = mass / molar mass = 3.25 kg / 0.05585 kg/mol
Next, we need to find the number of atoms in the block. Since each mole contains 6.022 × 10^23 atoms, we can multiply the number of moles by Avogadro's number:
Number of atoms = number of moles × Avogadro's number
Finally, multiply the number of atoms by the number of electrons per atom. Iron has an atomic number of 26, which means each iron atom has 26 electrons:
Number of electrons = number of atoms × 26
2. Calculate the charge of a single electron:
The elementary charge (charge of an electron) is approximately 1.602 × 10^(-19) C.
3. Find the fraction of electrons that need to be removed:
Divide the desired charge of the block by the charge of a single electron to find the number of electrons required to be removed:
Number of electrons to be removed = desired charge / charge of a single electron
Finally, divide the number of electrons to be removed by the total number of electrons in the block to get the fraction:
Fraction of electrons to be removed = number of electrons to be removed / number of electrons in the block
By following these steps and performing the necessary calculations, you will be able to determine the fraction of electrons that need to be removed from the iron block.