### Degeneracy

Posted:

**Mon Feb 04, 2019 3:07 pm**Could someone explain what degeneracy tells us and how it can be used? I am still unclear on the topic.

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=128&t=41364

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Posted: **Mon Feb 04, 2019 3:07 pm**

Could someone explain what degeneracy tells us and how it can be used? I am still unclear on the topic.

Posted: **Mon Feb 04, 2019 3:16 pm**

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.

Posted: **Mon Feb 04, 2019 3:16 pm**

Degeneracy is the number of ways of achieving a given energy state, and can be found by relation of the Boltzmann equation.

Posted: **Mon Feb 04, 2019 3:22 pm**

Degeneracy (W) is the number of ways of achieving a given energy state. This value is important because when using the Blotzman equation S=kB lnW, degeneracy can help find the entropy of the system.

Posted: **Mon Feb 04, 2019 3:53 pm**

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.

Posted: **Mon Feb 04, 2019 4:29 pm**

In essence, degeneracy refers to how many states available for one energy level. For example, in class, we briefly spoke about the molecule CH_{3}Cl. As the Cl atom can be in one of four different locations (as the CH_{3}Cl molecule is tetrahedral), it has a degeneracy of 4. However, the molecule CH_{4} has a degeneracy of one simply because all the configurations for the molecule are the same (central carbon and four hydrogens).

Posted: **Thu Feb 07, 2019 3:48 pm**

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?

Posted: **Sat Feb 09, 2019 5:08 pm**

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?

Posted: **Mon Feb 11, 2019 10:08 am**

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.