Find the potential energy, V(r), and the magnitude of the force, | F |, associated with:
(a) the interaction between a proton and an electron separated by a distance of 0.529 Å
(b) the interaction between the nucleus of Neon (Ne) and an electron separated by a distance of 2 Å.
(c) the interaction between two electrons within a p orbital (separated by 1 Å)
To find the potential energy, V(r), and the magnitude of the force, |F|, for the interactions mentioned, we need to use Coulomb's Law.
Coulomb's Law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for the magnitude of the force, |F|, is given by:
|F| = k * (|q1| * |q2|) / r^2
where |F| is the magnitude of the force,
k is Coulomb's constant (k = 8.988 × 10^9 Nm^2/C^2),
|q1| and |q2| are the magnitudes of the charges of the two particles, and
r is the distance between the particles.
To determine the potential energy, V(r), we need to integrate the force function with respect to distance, as potential energy is the negative integral of the force function. The potential energy is dependent on the relative position between the two particles.
(a) Interaction between a proton and an electron separated by a distance of 0.529 Å:
Given that a proton has a charge of +1.602 × 10^-19 C and an electron has a charge of -1.602 × 10^-19 C, and the distance between them is 0.529 Å (1 Å = 1 × 10^-10 m), we can substitute these values into the Coulomb's Law formula:
|F| = k * (|q1| * |q2|) / r^2
= (8.988 × 10^9 Nm^2/C^2) * (-1.602 × 10^-19 C * 1.602 × 10^-19 C) / (0.529 × 10^-10 m)^2
After calculating |F|, to find the potential energy, V(r), you need to integrate the force function over the distance, which requires an initial reference point.
(b) Interaction between the nucleus of Neon (Ne) and an electron separated by a distance of 2 Å:
For this interaction, you would follow the same process as in the previous example. Substitute the charge values (the charge of the nucleus and the charge of the electron) and the distance value (2 Å) into the Coulomb's Law formula to calculate |F|. Then, integrate the force function to find the potential energy, V(r).
(c) Interaction between two electrons within a p orbital separated by 1 Å:
Similar to the previous examples, substitute the charge values (charge of an electron) and distance value (1 Å) into the Coulomb's Law formula to calculate |F|. Then, integrate the force function to find the potential energy, V(r).
Remember, in all these cases, the potential energy will be negative for attractive forces and positive for repulsive forces.