Answer:
a) F = -1.82 10⁻¹⁵ N, b) K = 9.1 10⁻¹⁶ J
Explanation:
a) To calculate the force between the nucleus and the electrons, let's use the Coulomb equation
F = k q Q / r²
as the nucleus occupies a very small volume compared to electrons, we can suppose it as punctual
let's calculate
F = 9 10⁹ (-1.6 10⁻¹⁹) (79 1.6 10⁻¹⁹) / (10⁻¹⁰)²
F = -1.82 10⁻¹⁵ N
b) they ask us for kinetic energy
let's use Newton's second law
F = m a
acceleration is centripetal
a = v² / r
we substitute
F = m v² / r
v = √ (F r / m)
v = √ (1.82 10⁻¹⁵ 10⁻¹⁰ / 9.1 10⁻³¹)
v = √ (0.2 10⁻¹⁶)
v = 0.447 10⁸ m / s
kinetic energy is
K = ½ m v²
K = ½ 9.1 10⁻³¹ (0.447 10⁸)²
K = 0.91 10⁻¹⁵ J
K = 9.1 10⁻¹⁶ J
Answer:
This can be translated to:
"find the electrical charge of a body that has 1 million of particles".
First, it will depend on the charge of the particles.
If all the particles have 1 electron more than protons, we will have that the charge of each particle is q = -e = -1.6*10^-19 C
Then the total charge of the body will be:
Q = 1,000,000*-1.6*10^-19 C = -1.6*10^-13 C
If we have the inverse case, where we in each particle we have one more proton than the number of electrons, the total charge will be the opposite of the one of before (because the charge of a proton is equal in magnitude but different in sign than the charge of an electron)
Q = 1.6*10^-13 C
But commonly, we will have a spectrum with the particles, where some of them have a positive charge and some of them will have a negative charge, so we will have a probability of charge that is peaked at Q = 0, this means that, in average, the charge of the particles is canceled by the interaction between them.