Quantums numbers & the probability of where an electron may be found

Definations 1- A quantum of energy is the amount of energy required to move an electron from one energy level to another. Photons are bundles غير مجزء2- Photon:- of light energy that is emitted by electrons as they go from higher energy levels to lower levels

Excited State and Ground State 3- Ground state: the lowest possible energy level an electron be at. 4- Excited state: an energy level higher than the ground state. 5- Emission Spectrum: Light emitted produces a unique emission spectrum

Hydrogen Emission Spectrum Violet Blue Red Balmer Series

Bohr Model for Hydrogen

The Bohr model explained the emission spectrum of the hydrogen atom but did not always explain those of other elements.

Quantum Mechanical Model 1920’s Werner Heisenberg (Uncertainty Principle) Louis de Broglie (electron has wave properties) Erwin Schrodinger (mathematical equations using probability, quantum numbers)

Davisson and Germer confirmed de Broglie’s hypothesis for electrons. Electrons produced a diffraction pattern similar to x-rays.

Erwin Schrodinger, 1925 Quantum (wave) Mechanical Model of the Atom 6- Quantum Numbers:- specify the properties of atomic orbitals and their electrons , there are Four quantum numbers are required to describe the state of the hydrogen atom. 7- Atomic Orbital:- A region in space in which there is high probability of finding an electron 10

The Four Quantum Numbers Principal Quantum Number Orbital Quantum Number Magnetic Quantum Number Spin Quantum Number

1- Principal Quantum Number, n 1- Indicates main energy levels n = 1, 2, 3, 4… 2- Each main energy level has sub-levels 3- The maximum number of electrons in a principal energy level is given by = 2n2 Where, n= the principal quantum number

2- Orbital Quantum Number, ℓ (Angular Momentum Quantum Number) Indicates shape of orbital sublevels ℓ = n-1 ℓ sublevel 0 s 1 p 2 d 3 f 4 g

f orbitals

3- Magnetic Quantum Number, ml Indicates the orientation of the orbital in space. Values of ml : integers -l to l The number of values represents the number of orbitals. Example: for l= 2, ml = -2, -1, 0, +1, +2

4- Electron Spin Quantum Number, (ms or s) Indicates the spin of the electron (clockwise or counterclockwise). Values of ms: +1/2, -1/2

Example Answer: n=3 l = 2 ml = -2,-1, 0, +1, +2 Q:- List the values of the four quantum numbers for orbital in the 3d sublevel. Answer: n=3 l = 2 ml = -2,-1, 0, +1, +2 ms = +1/2, -1/2 for each pair of electrons

8- The Electron Cloud The electron cloud represents positions where there is probability of finding an electron.

The higher the electron density, the higher the probability that an electron may be found in that region.

The Electron Cloud for Hydrogen 90% probability of finding the electron within this space

Probability Curve for Hydrogen

Schrodinger’s Equations probability of where an electron may be found y is called the wave function and indicates the probability of where an electron may be found.

From Quantum Mechanical Model can obtained that the following:- 1- Electrons are located in specific energy levels. 2- there is no exact path around the nucleus. 3- The model estimates the probability of finding an electron in a certain position.

Thank you for all attention & follow 9-3-2014