Dimensions of Angular and Radial Nodes

In summary, radial and angular nodes are regions where the wavefunction is zero, but they are not infinitesimal points in space. They are actually subspaces with a size of zero in the mathematical sense, but this size increases to near infinity when considering realistic wavefunctions. The term "epsilon" is used to represent a small non-zero real number, and for any probability greater than zero, there is a corresponding volume where the wave function is less than the square root of epsilon.
  • #1
sams
Gold Member
84
2
Radial and angular nodes are simply a region where the wavefunction is zero. But speaking about their dimensions, do they have any thickness or are they just an infinitesimal point in space without dimensions?

Thanks a lot!
 
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  • #2
They are not points but subspaces. And size zero in math sense. As soon as you give an ##\epsilon>0## for the maximum probability density, that size shoots up to (near?) infinity for all realistic wavefunctions.
 
  • #3
BvU said:
ϵ
What epsilon stands for?
 
  • #4
A non-zero real number, as in 'for any probability ## \epsilon ## > 0 there is a volume > 0 where the wave function is < ##\sqrt \epsilon##'

usually ## \epsilon## means very small
 

Related to Dimensions of Angular and Radial Nodes

What is the difference between angular and radial nodes?

Angular nodes refer to the regions of space where the probability of finding an electron is zero due to the angular momentum of the electron. Radial nodes, on the other hand, refer to the regions of space where the probability of finding an electron is zero due to the radial distance from the nucleus.

How do angular and radial nodes affect the shape of an atomic orbital?

Angular nodes determine the shape of the orbital, while radial nodes determine the size. The number of angular nodes also determines the number of lobes in an orbital, with one lobe for each angular node.

What is the relationship between the number of angular and radial nodes in an orbital?

The number of angular nodes is always one less than the number of radial nodes. For example, if an orbital has 3 radial nodes, it will have 2 angular nodes.

Why are angular and radial nodes important in atomic structure?

Angular and radial nodes play a crucial role in determining the energy levels and electronic configurations of atoms. The number of nodes also affects the reactivity and chemical properties of elements.

How can the number of angular and radial nodes be determined experimentally?

The number of angular nodes can be determined by the quantum number l, while the number of radial nodes can be determined by the principal quantum number n. These quantum numbers can be obtained through spectroscopic techniques, such as photoelectron spectroscopy or emission spectroscopy.

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