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Basically, degeneracy is the number of states in which energy can be at a given level. If a given particle can only be at a certain energy level in one particular state (i.e. if it moves, its energy level changes), then it has a degeneracy of 1. Going back to the example Professor Lavelle gave in class, if a particle can exist at the same energy level on both the right side and the left side of a flask, it has a degeneracy of 2, because there are two ways in which it can be at one energy level. Degeneracy can be used to calculate entropy, and if we know that there is a high degeneracy, we also know that there is high entropy.
In essence, degeneracy refers to how many states available for one energy level. For example, in class, we briefly spoke about the molecule CH3Cl. As the Cl atom can be in one of four different locations (as the CH3Cl molecule is tetrahedral), it has a degeneracy of 4. However, the molecule CH4 has a degeneracy of one simply because all the configurations for the molecule are the same (central carbon and four hydrogens).
Patrick Cai 1L wrote:A good equation mentioned today in lecture for calculating the number of possible degenerate state was the formula , useful to determining all possible microstates of different and separate particles.
Does W = 2^n apply specifically to the problem we did in class? Or is it a general formula?
105169446 wrote:I am still confused as to what exactly the difference between degeneracy and entropy? Don't both of these concepts relate to disorder in a system?
While both of them relate to disorder, degeneracy is just the number of states a system has that are the same energy level. Entropy, however, is the degree of disorder in a system. Entropy can be calculated using degeneracy in the equation S = Kb x ln(W). The higher the degeneracy a system has, the higher its maximum entropy will be, because it will have many different possible states and can be very disordered.
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