9. Quantum Mechanics

Quantum Numbers: Nodes

How to Determine Number of Angular Nodes, Radial Nodes, and Total Nodes of Orbitals Examples

Which atomic orbital has the fewest angular nodes? &nbsp;

Types of Nodes and Quantum Numbers | Practice Exam 3.1 | Fall 2021

Consider a fictitious one-dimensional system with one electron.
The wave function for the electron, drawn below, is
c1x2 = sin x from x = 0 to x = 2p. (b) At what value or
values of x will there be the greatest probability of finding the
electron? 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/c414757615008564-1660752692817.jpg" alt="" />

(a) With reference to Figure 6.19, what is the relationship
between the number of nodes in an s orbital and the value
of the principal quantum number?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/21927baf3a6bf418-1664384193404.jpg" alt="" />

Quantum Numbers: Nodes Example 2

The Shapes of Atomic Orbitals

How many nodal surfaces does a 4s orbital have? Draw a cutaway representation of a 4s orbital showing the nodes and the regions of maximum electron probability.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/8c5104249357ad11-1669853932744.jpg" alt="" />

Quantum Numbers: Nodes Example 1

Which atomic orbital has the greatest number of radial nodes?

Nodes and Quantum Numbers

Figure 7.4 shows the radial probability distribution functions
for the 2s orbitals and 2p orbitals. (a) Which orbital,
2s or 2p, has more electron density close to the nucleus?<img src="https://lightcat-files.s3.amazonaws.com/problem_images/826ce20729b851c9-1660757071133.jpg" alt="" />

SHAPES OF ATOMIC ORBITALS - S, P, D and F

The accompanying drawing shows a contour plot for a dyz 
orbital. Consider the quantum numbers that could potentially 
correspond to this orbital. 
(d) The probability density goes to zero along which of the 
following planes: xy, xz, or yz? 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/e405e332b390a3e3-1660833821260.jpg" alt="" />

(b) Identify the number 
of nodes; that is, identify places where the electron density 
is zero, in the 2px orbital; in the 3s orbital.

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Wavelength and Frequency

Wavelength&nbsp;is the distance from one crest of a wave to another, whereas frequency is the number of waves within a second.&nbsp;

Quantum Numbers: Spin Quantum Number

The Spin Quantum Number deals with the spin of an electron within an orbital.

Speed of Light

The Speed of Light in a vacuum is related to the wavelength and frequency of a light particle.

Bohr Equation

In the Bohr Equation, the energy and wavelength a photon is related to its energy shell transitions.

Quantum Numbers: Angular Momentum Quantum Number

The&nbsp;Angular Momentum Quantum Number&nbsp;gives the shape of the atomic orbitals.

Emission Spectrum

Emission Spectra is a series of lines formed when emitted light is focused by a slit and passed through a prism. &nbsp;

Introduction to Quantum Mechanics

The 4 Quantum Numbers provide us the coordinates to find the theoretical location of an electron.

A node is the region in an atom with zero electron density and where an electron is least likely to exist.

The Energy of Light

The Energy of Light&nbsp;involves the use of a new variable Planck's Constant.

Electromagnetic Spectrum

The Electromagnetic Spectrum is the different forms of radioactive energy that exists in our universe.

Heisenberg Uncertainty Principle

Heisenberg's Uncertainty Principle&nbsp;tries to explain the potential duality of an electron behaving as either a particle or wave.&nbsp;

Quantum Numbers: Number of Electrons

The Quantum Numbers can give both the quantity and location of electrons within a given atom.&nbsp;

Quantum Numbers: Principal Quantum Number

The Principal Quantum Number gives both the size and energy of an electron shell.&nbsp;

Photoelectric Effect

What happens when light strikes the surface of a metal? The Photoelectric Effect&nbsp;can help to explain that.&nbsp;

Quantum Numbers: Magnetic Quantum Number

The Magnetic Quantum Number gives the location of an electron within a specific orbital.

Bohr Model

In the Bohr Model, electrons can move up and down to different orbitals or shells based on absorbing or releasing of energy.&nbsp;

De Broglie Wavelength

The&nbsp;De Broglie Wavelength equation relates wavelength to velocity or speed.&nbsp;

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