Two identical iron spheres have equal positive charges and the force between them when they are 1.4 m apart is 1.4 N.What percentage of the electrons has been removed from each sphere if each sphere has 1 mole (6 × 10²³) of iron atoms? (k_e = 8.99 × 10⁹ N⋅m²/C²,the atomic number of iron is 26,and the electron charge is −1.6 × 10−¹⁹ C)

Question

Quizplus · Accepted Answer

First, we can calculate the charge of each sphere using Coulomb's law:

F = (k * q^2) / d^2

1.4 N = (8.99 * 10^9 N*m^2/C^2) * (q^2) / (1.4 m)^2

Solving for q, we get:

q = 6.38 * 10^-17 C

Next, we can calculate the number of electrons in one sphere using the atomic number of iron:

1 mole * (6.022 * 10^23 atoms/mol) = 6.022 * 10^23 atoms

6.022 * 10^23 * 26 = 1.565 * 10^25 electrons

If we assume that x% of these electrons have been removed, we can calculate the new charge of one sphere:

new charge = (1 - x/100) * 1.602 * 10^-19 C * 1.565 * 10^25

Now we can use Coulomb's law again to calculate the new force between the spheres:

1.4 N = (8.99 * 10^9 N*m^2/C^2) * [(new charge)^2] / (1.4 m)^2

Plugging in the expressions for new charge and solving for x, we get:

x = 7 * 10^-10 %

Rounded to the nearest integer, this gives us a final answer of D: 7 * 10^-10 %, which is equivalent to 7 * 10^-12.

Two Identical Iron Spheres Have Equal Positive Charges and the Force