cohesive energy problem

In the videos about DFT, we carefully defined the physical meaning of the concept total energy. If you did the tasks in the “let’s play” module of this course, you also know how to calculate the total energy for a given crystal. A related concept is the cohesive energy of a crystal (also known as atomization energy). It is defined as the difference between the total energy of all atoms that make up a given amount of material, all of these atoms being free isolated atoms, and the total energy of the same number and type of atoms being in the crystal. This can be expressed per unit cell, per atom, per formula unit, per mole, … :

E_cohesive = E_atoms – E_crystal

The experimental value of the cohesive energy of rocksalt (common table salt) is 187 kcal/mol. Is that large or small? The next exercise — in the style of an open classical physics problem — is meant to get a feeling for the size of cohesive energies. Here it goes:

Imagine yourself to be in a room, say a typical living room or class room. You get a box with free sodium atoms (Na) and another box with free chlorine atoms (Cl). (I know, this is quite hypothetical, it wouldn’t be easy to really prepare such boxes with free atoms — but let’s assume…) You connect the two boxes, and let the atoms react with each other. The result is one teaspoon of rocksalt. How much has the temperature of the room increased?

Do you have enough information to answer this question? Yes, you have — provided you make some order of magnitude estimations and some other idealizations that are common in physics problems. Give it a try, write down your answer in a pdf file (this can be a scan of a hand-written page as well), and submit it hereafter. The reasoning is more important than the exact numerical answer, but I bet you can end up in the right ball park. Don’t spend hours on it, yet give it a fair try.

By the way, this might be a good to practice your LaTeX writing skills (relevant for those among you who are working on the project for this course). Look here for instructions to write your answer to this question using an online LaTeX editor, which will produce a neat pdf file to submit. If you are not interested in using LaTeX right now, you can make a pdf in any other way you prefer — no problem.