# What is degeneracy as opposed to a degenerate state? How can we know what orbitals are higher in energy?

##### 1 Answer

This is a kind of complicated question.

- A
**degenerate state**is a state in which the energy is the same as other states. - A
**degeneracy**is the number of states that have that same energy, and is described as#2l+1# .

*So, the difference is that degeneracy describes how many states, and a degenerate state is specifically which ones count.*

- Any
#ns# orbital is the same energy for the same#n# . - No,
#p# and#d# orbitals of the same#n# don't necessarily have the same energy (not even in hydrogen atom). - I cannot tell you the energy of every orbital, because their energies change throughout the periodic table, and sometimes the actual ordering is different.

**DEGENERATE STATES**

** Atomic** orbitals that share the

*same*principal quantum number

*necessarily*degenerate. They are called

**degenerate states**.

(if they share the same *same* orbital!)

On the other hand, if their *differ*, they might be *degenerate by coincidence*, but they are *not* necessarily degenerate.

For example, the

- They do not have the same shape (different
#l# ). - They do not have the same total number of radial nodes (different
#n - l - 1# ). - They do not have the same number of angular (planar) nodes (different
#l# ). - Maybe some combination of all three.

However, the

One might call them degenerate once the energies get close enough. When comparing their *counteracting* (lower *degenerate by coincidence*".

**DEGENERACY**

Like I said, degeneracy is just the number of orbitals of the same energy. Typically we say, for example:

- The
#np# atomic orbitals are, because there are*triply degenerate***three**of them in a free atom, and they are all equivalent orbitals with equivalent energies. - The
#np# atomic orbitals have aof*degeneracy*#2l + 1 = 3# , since their#l# is equal to#1# .

For example, a

#ul(uarr darr) " " ul(uarr color(white)(darr)) " " ul(uarr color(white)(darr))#

#underbrace(" "" "" "" "" "" "" "" ")#

#2p_x" "" "2p_y" "" "2p_z#