2 1g carbon disks 1cm apart have opposite charges of equal magnitude such that there is a 1*10^-5 N force between them. Calculate ratio of excess electrons to total atoms on the negatively charged disk.

To find the ratio of excess electrons to total atoms on the negatively charged disk, we need to start by determining the number of excess electrons that create the given force between the two charged disks. We can use Coulomb's law, which describes the electrostatic force between two charges. Let's break this down step by step.

Coulomb's Law

Coulomb's law states that the force (F) between two point charges (q1 and q2) separated by a distance (r) is given by the formula:

F = k * (|q1 * q2|) / r²

Here, k is Coulomb's constant, approximately equal to 8.99 x 10^9 N m²/C².

Given Values

• Force (F) = 1 x 10^-5 N
• Distance (r) = 1 cm = 0.01 m
• Coulomb's constant (k) = 8.99 x 10^9 N m²/C²

Calculating the Charge

We can rearrange Coulomb's law to solve for the product of the charges:

|q1 * q2| = F * r² / k

Since the disks have equal and opposite charges, we can denote them as q. Thus, we have:

|q|² = F * r² / k

Substituting the values:

|q|² = (1 x 10^-5 N) * (0.01 m)² / (8.99 x 10^9 N m²/C²)

|q|² = (1 x 10^-5) * (1 x 10^-4) / (8.99 x 10^9)

|q|² = 1 x 10^-9 / 8.99 x 10^9

|q|² ≈ 1.11 x 10^-19 C²

Taking the square root gives us:

|q| ≈ 1.05 x 10^-10 C

Finding the Number of Excess Electrons

The charge of a single electron is approximately 1.6 x 10^-19 C. To find the number of excess electrons (n), we can use the formula:

n = |q| / e

Substituting the values:

n = (1.05 x 10^-10 C) / (1.6 x 10^-19 C/electron)

n ≈ 6.56 x 10^8 electrons

Calculating the Total Number of Atoms

To find the total number of atoms on the negatively charged disk, we need to know its mass and the atomic mass of the material. Assuming the disk is made of carbon, with an atomic mass of about 12 g/mol, we can estimate the number of atoms.

Let's say the disk has a mass of 1 g. The number of moles of carbon in 1 g is:

moles = mass / atomic mass = 1 g / 12 g/mol = 0.0833 mol

Using Avogadro's number (approximately 6.022 x 10^23 atoms/mol), we can find the total number of atoms:

total atoms = moles * Avogadro's number

total atoms = 0.0833 mol * 6.022 x 10^23 atoms/mol ≈ 5.01 x 10^22 atoms

Calculating the Ratio

Now that we have both the number of excess electrons and the total number of atoms, we can find the ratio:

ratio = excess electrons / total atoms

ratio = (6.56 x 10^8) / (5.01 x 10^22)

ratio ≈ 1.31 x 10^-14

This means that the ratio of excess electrons to total atoms on the negatively charged disk is approximately 1.31 x 10^-14, indicating that there are very few excess electrons compared to the total number of atoms in the disk.