Two alpha particles (helium nuclei), each consisting of two protons and two neu- trons, have an electrical potential energy of 6.08×10−19 J.

What is the distance between these par- ticles at this time? The Coulomb constant is 8.98755 × 109 N · m2/C2, the elemental charge is 1.6021 × 10−19 C, and the eration due to gravity is 9.8 m/s2.
Answer in units of m.

Well, let's see. We can use the formula for electrical potential energy:

PE = k * (q1 * q2) / r

where PE is the electrical potential energy, k is the Coulomb constant, q1 and q2 are the charges of the particles, and r is the distance between them.

In this case, since we have two alpha particles, we're dealing with two charges of 2 * (1.6021 × 10^-19 C).

Let's plug in the numbers:

6.08×10^-19 J = (8.98755 × 10^9 N · m^2/C^2) * (2 * (1.6021 × 10^-19 C) * (1.6021 × 10^-19 C)) / r

Simplifying the equation, we get:

r = (8.98755 × 10^9 N · m^2/C^2 * 2 * (1.6021 × 10^-19 C) * (1.6021 × 10^-19 C)) / 6.08×10^-19 J

Do some more math magic and we'll find:

r = 1.2 * 10^-15 J / N·m^2·C^2

Now, we can chuck these numbers into the equation and find the value for r.

But you know what? Instead of giving you the long, boring answer, let me throw some clown humor your way:

Why did the alpha particle visit his therapist?

Because he was going through potential energy anxiety!

Okay, okay. I'll give you the serious answer too: the distance between these particles is approximately 1.2 × 10^-15 meters.

To find the distance between the two alpha particles, we can use Coulomb's law, which states:

Electrical potential energy = (Coulomb's constant * charge of particle 1 * charge of particle 2) / distance

Given information:
Electrical potential energy = 6.08 × 10^(-19) J
Coulomb's constant = 8.98755 × 10^9 N · m^2/C^2
Charge of alpha particle = 2 * (charge of proton) = 2 * 1.6021 × 10^(-19) C
Acceleration due to gravity = 9.8 m/s^2

Substituting the values into the equation, we have:

6.08 × 10^(-19) J = (8.98755 × 10^9 N · m^2/C^2) * (2 * 1.6021 × 10^(-19) C)^2 / distance

Simplifying the equation:

6.08 × 10^(-19) J = (8.98755 × 10^9 N · m^2/C^2) * (2 * 1.6021 × 10^(-19) C)^2 / distance

Now, let's solve for the distance:

distance = (8.98755 × 10^9 N · m^2/C^2) * (2 * 1.6021 × 10^(-19) C)^2 / 6.08 × 10^(-19) J

distance = (8.98755 × 10^9 * 2 * 1.6021 × 10^(-19))^2 / 6.08 × 10^(-19)

distance = (2.8822 × 10^(-9))^2 / 6.08 × 10^(-19)

distance = 8.30324 × 10^(-18) / 6.08 × 10^(-19)

distance = 13.645 m

Therefore, the distance between the two alpha particles is 13.645 meters.

To find the distance between the two alpha particles, we can equate the electrical potential energy to the electrical potential energy formula using the Coulomb constant and the charges of the particles. The electrical potential energy formula is:

U = (k * q1 * q2) / r

Where:
U is the electrical potential energy.
k is the Coulomb constant (8.98755 × 10^9 N · m^2/C^2).
q1 and q2 are the charges of the particles.
r is the distance between the particles.

In this case, the two alpha particles have the same charge because they are both helium nuclei. Each alpha particle has a charge of 2e, where e is the elementary charge (1.6021 × 10^-19 C). So, q1 = q2 = 2e.

Now, we can rearrange the equation to solve for the distance r:

r = (k * q1 * q2) / U

Substituting the given values:

r = (8.98755 × 10^9 N · m^2/C^2 * 2e * 2e) / (6.08 × 10^-19 J)

To simplify, we can convert elementary charge 'e' to coulombs:
1e = 1.6021 × 10^-19 C
So, 2e = 2 * (1.6021 × 10^-19 C)

r = (8.98755 × 10^9 N · m^2/C^2 * (2 * 1.6021 × 10^-19 C) * (2 * 1.6021 × 10^-19 C)) / (6.08 × 10^-19 J)

Performing the calculation, we get:

r = 2.4282 × 10^-15 m

Therefore, the distance between the particles at this time is approximately 2.4282 × 10^-15 meters.

Well, leave one particle alone, put the other at infinity (zero PE), and bring it to position d from the other. The work done must be the PE of the system.

Work=force*distance
= INTegral kqq/x^2 dx= -kqq/x over limits
= =kqq/inf - (-kqq/d)

or d= kqq/electricalPE

you have the numbers given, solve for d.
In my google search window, I entered..
((8.89E9)(1.60E-19)^2)/(6.08E-19)=

Now that is the distance. You do not need g except to ponder why it was given.