Excess electrons are placed on a small lead sphere with mass 8grams so that its net charge is -3.20*10^9C.
a) Find the number of excess electrons on the lead sphere
b) How many electrons are there per lead atom
(a) N=q/e=3.2•10⁹/1.6•10⁻¹⁹= 2•10²⁸
(b)
The mass of one lead atom is
m₀=207.2 amu =207.2•1.67•10⁻²⁷=3.46•10⁻²⁵kg
The number of atoms in 8 g of lead
N₀=m/m₀=0.008/3.46•10⁻²⁵ = 2.31•10²³
N/N₀=2•10²⁸/2.31•10²³=8.65•10⁵
To solve this problem, we need to calculate the number of excess electrons on the lead sphere and then determine the number of electrons per lead atom.
a) To find the number of excess electrons on the lead 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 elementary charge.
Rearranging the formula, we get:
n = q / e
Given that the charge q is -3.20 * 10^9 C and the elementary charge e is 1.6 * 10^-19 C, we can substitute these values into the formula:
n = (-3.20 * 10^9 C) / (1.6 * 10^-19 C)
Simplifying, we get:
n = -2.0 * 10^28 electrons
Therefore, the number of excess electrons on the lead sphere is -2.0 * 10^28 electrons.
b) To find the number of electrons per lead atom, we need to know the number of lead atoms present in the sphere. The relationship between mass and the number of atoms is given by Avogadro's number:
N = m / (M * u)
where N is the number of atoms, m is the mass, M is the molar mass, and u is the atomic mass unit.
The molar mass of lead (Pb) is 207.2 g/mol, and the atomic mass unit (u) is 1.66 * 10^-24 g. The mass of the lead sphere is 8 g. Substituting these values into the formula:
N = (8 g) / (207.2 g/mol * (1.66 * 10^-24 g))
Simplifying, we get:
N ≈ 1.72 * 10^23 atoms
To calculate the number of electrons per lead atom, we divide the number of excess electrons by the number of lead atoms:
Number of electrons per lead atom = (Number of excess electrons)/(Number of lead atoms)
Number of electrons per lead atom = (-2.0 * 10^28 electrons) / (1.72 * 10^23 atoms)
Simplifying, we get:
Number of electrons per lead atom ≈ -116 electrons
Therefore, there are approximately 116 excess electrons per lead atom on the sphere.
To answer these questions, we need to understand the concepts of charge, electrons, and the properties of lead atoms.
a) Finding the number of excess electrons on the lead sphere:
We know that the net charge of the small lead sphere is -3.20*10^9C, and we need to find the number of excess electrons on it.
1. Start with the elementary charge, denoted as 'e,' which is equal to -1.60*10^(-19) coulombs. This value represents the charge carried by a single electron.
2. Divide the total charge of the sphere (-3.20*10^9C) by the elementary charge (-1.60*10^(-19)C) to find the number of excess electrons.
Number of excess electrons = (-3.20*10^9C) / (-1.60*10^(-19)C)
3. Calculate this value using a calculator, which yields the number of excess electrons on the lead sphere.
b) Finding the number of electrons per lead atom:
To determine the number of electrons per lead atom, we need to know the atomic number or the number of nucleons (protons and neutrons) within the atom. However, since we are provided with the mass of the lead sphere, we can estimate the number of lead atoms in it based on the molar mass of lead.
1. Find the molar mass of lead using the periodic table or reliable sources. The molar mass of lead (Pb) is approximately 207.2 grams/mol.
2. Convert the mass of the lead sphere, which is 8 grams, to moles by dividing it by the molar mass.
Moles of lead = (8g) / (207.2g/mol)
3. Next, we need to determine Avogadro's number denoted as 'N.' Avogadro's number represents the number of entities (atoms, molecules, etc.) in one mole, and it is approximately 6.022*10^23.
4. Multiply the moles of lead by Avogadro's number to find the number of lead atoms in the sphere.
Number of lead atoms = (moles of lead) * Avogadro's number
5. Lastly, to find the number of electrons per lead atom, we need to know that a lead atom is neutral, meaning it has the same number of electrons as protons.
Number of electrons per lead atom = Number of lead atoms
By following these steps, you can calculate the desired quantities accurately. Make sure to double-check any values or constants used for the calculations to ensure accuracy.