explain all you can about the properties of the atoms using the laws that electr
ID: 1501204 • Letter: E
Question
explain all you can about the properties of the atoms using the laws that electrons obey ( pauli exclusion principle, schrodingers equation, and coulomb's law), the radial probability curves, and the fact that closed s and p orbitals are spherically symmetrical. Please also write down any information about the element's activity ionization and shape in the periodic table if possible p.s I know I ask too much for you guys to do it, but plz try your best to explain this question to me. Thank you so much
Explanation / Answer
The Pauli exclusion principle is part of one of our most basic observations of nature: particles of half-integer spin must have antisymmetric wavefunctions, and particles of integer spin must have symmetric wavefunctions.
The nature of the Pauli exclusion principle can be illustrated by supposing that electrons 1 and 2 are in states a and b respectively. The Pauli Exclusion Principle states that, in an atom or molecule, no two electrons can have the same four electronic quantum numbers. As an orbital can contain a maximum of only two electrons, the two electrons must have opposing spins. This means if one is assigned an up-spin ( +1/2), the other must be down-spin (-1/2).
Electrons in the same orbital have the same first three quantum numbers, e.g., n=1, l=0, ml=0 for the 1s subshell. Only two electrons can have these numbers, so that their spin moments must be either ms=1/2 or ms=+1/2.
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is also often called the Schrödinger wave equation, and is a partial differential equation that describes how the wavefunction of a physical system evolves over time.
The solution to the equation is based on the method of Eigen Values devised by Fourier. This is where any mathematical function is expressed as the sum of an infinite series of other periodic functions. The trick is to find the correct functions that have the right amplitudes so that when added together by superposition they give the desired solution.
The Schrodinger equation is the name of the basic non-relativistic wave equation used in one version of quantum mechanics to describe the behaviour of a particle in a field of force. There is the time dependant equation used for describing progressive waves, applicable to the motion of free particles. And the time independent form of this equation used for describing standing waves.
Coulomb's law, or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles .
Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.
The Coulomb's law equation provides an accurate description of the force between two objects whenever the objects act as point charges. A charged conducting sphere interacts with other charged objects as though all of its charge were located at its center. While the charge is uniformly spread across the surface of the sphere, the center of charge can be considered to be the center of the sphere. The sphere acts as a point charge with its excess charge located at its center.
Radial distribution curve gives an idea about the electron density at a radial distance from the nucleus. The value of 4r22 (radial probability density function) becomes zero at a nodal point, also known as radial node.
The number of radial nodes for an orbital = n-l-1.
Where n = principal quantum number and l= azimuthal quantum number.
When the wavefunction, , is squared the result is a number that is directly proportional to the probability of finding and electron at specific coordinate in 3D space. The radial portion of the wavefunction tells us if there is high or low probability at various distances from the nucleus .
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