Please show work and explain thought process. There are more parts to problem so
ID: 3893625 • Letter: P
Question
Please show work and explain thought process. There are more parts to problem so if these parts are done well I will ask those and give you max points for solutions.
Classical model of a van der Waals bond. In your chemistry classes, you learned that atoms (e.g. He. Ar, Xe) or non-polar molecules (e.g. N2- CH4. etc.) attract each other because of the random electric interactions of their electron clouds - this is called the van der Waals attraction and it is the reason why these substances form liquids or solids at low temperatures. Actually solving for the van der Waals interaction requires quantum mechanics, but using classical physics you can understand two important features: why the attractive force Is proportional to the inverse 7th power of their separation, and why it is stronger for bigger atoms or molecules. The simplified model that we will consider here Is as follows. Consider two neutral atoms or molecules A and B. separated by distance rAn- and each of radius R. We will consider each one to have an electron cloud with some random dipole moment pA rand and pB rand. due to the fact that at any one time the electrons may be in one or another part of the atom (remember: they have a probability distribution). We will use simple arguments based on what you know about atoms to figure out what this is. We will then assume that the electric field from each atom induces a dipole moment in the other: i.e. the electric field caused by pA rand in A produces an induced dipole pB rand in B. and vice versa. We will then figure out for the total dipole moments what is the average attractive force between the two atoms. Explain why. at large separations tad- it should be safe to consider only the dipole moments of the atoms, and why other moments (the monopole, quadruple. etc.) are being neglected. Suppose atom .4 is at position r.4 and D is at rjj- Show that if the response of atom B can be modeled as that of a conducting sphere of radius R. and the atoms are far enough apart that we can think of .4?s electric field as uniform near B. then pB ind = R3/r3Ab(3rAB PA rand)rAb-PA rand) where rAb = rB- rA is the separation vector.Explanation / Answer
Hi,
I have given a detailed step by step solution, giving my plan ahead at each step. I am unable to upload the images here for some reason. So, I am giving you the links for the images. Please do rate.
https://drive.google.com/file/d/0BzsApW5yffhsNkRpUWpKMjA1d00/edit?usp=sharing
https://drive.google.com/file/d/0BzsApW5yffhsS2ltQVFvQ0RVdVk/edit?usp=sharing
Cheers,
Saurav