Question

Electrons are placed on a small, 6 gram lead sphere, until the sphere possesses a net charge of -4.8 x10⁻⁹ C (or - 4.8 nC).

A. How many excess electrons are on this sphere?
B. How many excess electrons are on the sphere, per lead atom? The molar mass of lead is 207 grams/mol, and one mole consists of 6.02x10²³atoms).

Answer 1

The net charge of the sphere is -4.8 x10⁻⁹ C. There are approximately -3.0 x 10^10 excess electrons on the sphere. The number of excess electrons per lead atom is approximately -1.72 x 10^-12.

Step-by-step explanation:

In this question, we are given a small lead sphere with a net charge of -4.8 x10⁻⁹ C. To determine the number of excess electrons on the sphere, we can use the formula: Q = n * e, where Q is the charge, n is the number of excess electrons, and e is the charge of one electron (1.602 x 10^-19 C).

Using this formula, we can calculate the number of excess electrons on the sphere to be:

n = Q / e = (-4.8 x10⁻⁹ C) / (1.602 x 10^-19 C) = -3.0 x 10^10 electrons.

To find the number of excess electrons per lead atom, we need to divide the number of excess electrons by the number of lead atoms in the sphere. First, we need to convert the mass of the sphere to moles:

moles of lead = mass / molar mass = 6 g / 207 g/mol = 0.02899 mol.

Next, we can calculate the number of lead atoms:

number of lead atoms = moles of lead * Avogadro's number = (0.02899 mol) * (6.02 x 10^23 atoms/mol) = 1.743 x 10^22 atoms.

Finally, we can calculate the number of excess electrons per lead atom:

excess electrons per lead atom = number of excess electrons / number of lead atoms = (-3.0 x 10^10 electrons) / ( 1.743 x 10^22 atoms) = -1.72 x 10^-12 electrons per lead atom.