(a) What is the total negative charge, in coulombs, of all the electrons in a small 1.00 g sphere of carbon? One mole of C is 12.0 g, and each atom contains 6 protons and 6 electrons. (b) Suppose you could take out all the electrons and hold them in one hand, while the other hand you hold what is left of the original sphere. If you hold your hands 1.50 m apart at arms length, what force will each of them feel? Will it be attractive or repulsive?
To calculate the total negative charge of all the electrons in the small 1.00 g sphere of carbon, we need to follow a few steps:
(a) Calculate the number of carbon atoms in the sphere:
Using the molar mass of carbon, which is 12.0 g/mol, we can determine the number of moles of carbon in the sphere by dividing the mass of the sphere by the molar mass:
Number of moles of carbon = 1.00 g / 12.0 g/mol
Next, we need to convert the moles of carbon to the number of carbon atoms. Since one mole contains Avogadro's number of particles (6.022 x 10^23), we can multiply the number of moles of carbon by Avogadro's number to find the number of carbon atoms:
Number of carbon atoms = Number of moles of carbon × Avogadro's number
Now that we know the number of carbon atoms, we can find the total number of electrons by multiplying the number of carbon atoms by the number of electrons per carbon atom, which is 6:
Total number of electrons = Number of carbon atoms × 6
Finally, to find the total negative charge in coulombs, we need to multiply the total number of electrons by the elementary charge, denoted as e, which is approximately 1.602 x 10^-19 C:
Total negative charge = Total number of electrons × e
(b) To calculate the force between the two hands, we can use Coulomb's law, which states that the force between two charged particles is given by:
F = (k * |q1 * q2|) / r^2
Where F is the force, k is the electrostatic constant (k ≈ 8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, each hand will be holding the same number of electrons, so the charges are equal and opposite in sign. Therefore, q1 = -q2, and the force equation becomes:
F = (k * |q1^2|) / r^2
Since we know the charge on each electron is e, and we have calculated the total number of electrons, we can substitute these values into the equation. The distance between the hands, r, is given as 1.50 m.
Please note that the force will be attractive because the charges on the electrons and the remaining carbon sphere are opposite in sign.