I\'m having trouble answering a lot of these questions on my physics assignment!

Question

I'm having trouble answering a lot of these questions on my physics assignment! if you could help me out with the first two at least, i would really appreciate it! the graph they are referring to is the graph that is given right above. Thank you so much!!

In the activity you just completed in DL, you found that the average spacing of atoms/molecules in a gas at STP is about 10 particle diameters(~10 ). You also know from chemistry that the molecules of an ideal gas do not interact. Relate these two ideas, the average distance between gas molecule at STP, and the non-interaction between molecules of an ideal gas, to the particle-particle interaction model as represented by the PE graph. Now we want to analyze a physical system compressed of two particles. Look at pair-wise potential energy graph you received in DL. Suppose r is equal 1.2 . Suppose the particles are momentarily at rest at r = 1.2 (like a ball at the top of its trajectory when thrown straight up). What can you say about the total energy, Etot, and the subsequent motion of the two particles? Now suppose at the instant the particle have the separation 1.2 they have total KE equal to 0.1 What can you say about the total energy, Etot, and the subsequent motion of the two particles? You should have found that the total energy in(3.1-5, part b) s equal -0.8 epsilon. If the two particles in part b above are a closed system, what do you know about the total energy as their separation changes? In general, what is the minimum value of KE a system of particles can have? Use your response to the two previous parts of this question and the fact that the total energy is equal to -0.8 epsilon to determine the values of r where KE is minimum. Explain how your responses to all of the above determine the range of possible values of the separation of the two particles for this total energy. Your TA should have passed out a sheet with four graphs of the pair-wise potential energy. Plot, using the point-by-point method, Etotal and KE for two particles on these graphs for the following values of Etotal: - 0.4, -0.2, 0.0, and 0.2. (Reminder: point-by-point means using the relationship expressing energy conservation, picking particular values of r, and then calculating and plotting the KEs for those value of r.) Warning! Don't plot values of energies outside the allowed range of r(see 3.4-6, d) above.

Explanation / Answer

3.1-4) see this is the potential energy curve....

Force of interaction=-dU/dx

in simple terms slope tangent at any point of the given curve will give us the Force of interaction

now we see that as the distance between molecules increases the curve becomes more and more slant ultimately touching X-axis

this means that the slope keeps on decreasing

this means than force keeps on decreasing

thus, in the the case of ideal gasses the distance is as high as 10 atomic distance so the slope becomes nearly equal to zero

so there is no interaction between the molecules of inert gas

i hope it explaines some of your doubts

3.1-5)

a) as we can see from the graph energy of the particle is not at its minimum value at r=1.2*a

Etot=-0.9 epsilon

minimum energy lies at nearly r=1.1*a(see graph)

and we know that every system likes to minimize its energy

so it will drop ti "1.1" but in the process of dropping to "1.1" it will gain some kinetic energy so it will execute Simple harmonic motion around "1.1"

b) Etot=-0.9 epsilon +0.1 epsilon=0.8 epsilon

other arguements remain the same

it will like to come to the minimum energy point

and execute SHM about the minimum energy point.

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