How much work is required to bring two protons from an infinite distance of separation to 0.1 nm

How much work is required to bring two protons from an...

Key Concepts

Conversion from Particle Pair to Mole Quantities

When calculations involve single pair interactions and the result needs to be extended to a mole of such pairs, Avogadro's number is used to scale the energy from a single interaction to a mole of interactions. This conversion is critical in connecting microscopic calculations to macroscopic quantities.

SI Units and Energy Conversions

In problems like these, it is important to maintain consistency with SI units, such as using joules for energy, meters for distance, and coulombs for charge. Additionally, converting the energy from joules to kilojoules per mole involves using conversion factors such as dividing joules by 1000 to get kilojoules and multiplying by Avogadro's number to scale up to a mole.

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the electric force between two charges varies directly with the product of their charges and inversely with the square of the separation distance between them. This principle is essential in determining the work needed for moving charges in an electric field.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored by a pair of charges as a result of their positions relative to each other. It is calculated using the formula U = k * q1 * q2 / r, where k is Coulomb's constant, q1 and q2 are the charges, and r is the separation distance. It represents the work done to assemble the charges from infinity to a finite distance apart.

Transcript

00:04 This question asks us to calculate the work involved in moving two protons that are infinite distance from each other to a distance of 0 .1 nanometer from each other.

00:25 So we are given the protonic charge which is 1 .602 times 10 to the negative 19 couloms.

00:33 So that's the charge of a single proton.

00:35 And then we are told to calculate this using joules but because they say using the protonic charge we'll calculate also in joules per cool on and then we'll also convert it to kilojoules per mowls unit according to what's asked in the question so we have this equation we can use to calculate the work involved in this process so the work involved here can be calculated by using this equation, where it is equal to 1 over 4 ,5, phypsoyre knot, which is the permittivity of vacuum, and then epsilon r, which is the relative permittivity, or the dielectric constant.

01:32 And we have to multiply this by the charge of the first particle and by the charge of the second particle and then divide this by the distance between the particles which is r.

01:45 So here because we're not told the media that this is occurring in, we are going to assume that this is occurring in a vacuum.

01:56 So we can remove siren r because it's going to be one in that case.

02:01 And we can use this equation to calculate the work involved here.

02:06 So if we substitute epsiron knot with the value for that, which is 8 .854 times 10 to the negative 12, koulon squared, newton minus 1, meter minus 2.

02:31 Let me just write that here.

02:33 So you have access to that value 8 times 8 5, 4 times 10 to the negative 12, column square, newton minus 1, m per meter square.

03:00 So if we use that value and instead of q1 times q2, if we use q squared because we have two similar particles, which both have a charge of 1 .602 times 10 to the negative 19 coulum we get this and then instead of r i will have to use 0 .1 times 10 to the negative 9 meters so the distance between the particles is 0 .1 nanometer or if we convert that to the meters units it's going to be 0 .1 times 10 to the negative 9 meters so the distance between the particles is 0.

03:44 10 to the negative 9 meters...

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