# What contributes to the wall of an orbit?

##### 1 Answer

I'm not entirely sure what you (the invisible questioner) mean here, but here is an educated guess...

Here's what I think you're referring to.

**BOUNDARIES OF AN ORBITAL**

Not to be confused with an *orbit*, an ** orbital** is a region of electron density in the

**modern model of the atom**where the position of the electron is plotted as a probability density, a distribution over many measurements.

This is the

The darkest regions are where electrons are ** most likely** to be found. They are known as the

*most probable radial distance*[from the nucleus].

Anywhere outside an orbital is where electrons cannot be observed.

This is the result of how the wave function is defined in the **first postulate of quantum mechanics** (slightly modified from *Physical Chemistry: A Molecular Approach*, McQuarrie):

The state of a quantum-mechanical system is completely specified by a function#psi(vecr)# that depends on the coordinate of the particle. All possible information about the system can be derived from#psi(vecr)# .This function, called the wave function or the state function, has the important property that#psi^"*"(vecr)psi(vecr)d tau# is the probability that the particle lies in the [volume] interval#d tau# ,located at the [radial] position#vecr# .

An important note about this postulate is that ** where the system exists...** but the orbital

*is*the system here (specified by

The wave function

#overbrace(psi = psi(vecr))^"wave function", " "" "overbrace(0 < vecr < r_(max)," "0 < t < oo)^"domain"#

#overbrace(psi(0) = psi(r_(max)) = 0)^"boundary conditions"# ,#" "" "t = 0#

#overbrace(sfPsi(vecr,0) = Apsi(vecr))^"initial condition", " "" "overbrace(0 < vecr < r_(max))^"domain"# where

#r_(max)# is the radial distance of the orbital past which the orbital ceases to exist,#sfPsi = sfPsi(vecr,t)# is the time-dependentwave function, and#psi = psi(vecr)# is the time-independentwave function.

#A# is a normalization constant such that#int_(0)^(r_(max)) psi^"*"(vecr)psi(vecr)d tau = 1# .

And thus, the electron only exists until... there is no electron density to speak of, i.e. ** outside the orbital, the electron does not exist**.

**Hence, in quantum mechanics, the boundary of the orbital IS the "wall" of the orbital.**