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Chapter 7: Quantum Mechanical Model of the Atom

Nish C.'s project for Ms. Hubbel. Enriched Chem, period 2 Due Date: October 24th, 2012.
by

Nish Chankar

on 22 October 2012

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Transcript of Chapter 7: Quantum Mechanical Model of the Atom

By: Nish C.
For: Ms. Hubbel
E Chem, Period 2 Chapter 7:
The Quantum Mechanical
Model of the Atom Emission Spectra... INTRODUCTION What exactly IS Quantum Mechanics? Good Question... Let's ask our dear friend, Mr. Max Karl Ernst Ludwig Planck. He's been dead for over 50 years, but he's definitely a genius in this subject area. After all, he DID win the Nobel Prize in Physics for his discovery of the Quantum Theory, way back in 1918. Before my discoveries, people believed that all objects fell under the same physical laws (ie. The Classical Theory). No one stopped to think that maybe, a difference of size between two objects would affect how they physically operated. However, I discovered that 'small' objects, such as atoms and molecules, did indeed possess different properties, than, say, a horse or a person. Physicists before me neglected to account for the forces that hold atoms together. I was able to come up with The Quantum Theory - a theory that greatly altered the course of physics forever. Guten tag! Classical Theory -
The beginning of time - 1900

Quantum Theory -
1900 - Now 1947. Good ol' Maxie.....1858-1947 R.I.P. So, what exactly is a quantum? If I told you, I'd have to kill you. No, seriously...? Okay, fine! 'Quantum' is the latin word for "how many?". A quanta, in physics, is the minimum amount of any physical entity that is involved in an interaction. Dude, i STILL
don't get it..... Fine, fine. Here's an example ---> Now presenting....
the PHOTONS! Starring: Albert Einstein
(1879 - 1955) R.I.P. Einey, another good friend of ours, was the recipient of the Nobel Prize in Physics in 1921, for his solution to the mystery of the photoelectric effect. During his work on the photoelectric effect, Einey declared that each beam of light was made up of little particles. He subsequently named these particles photons.

Wait, but how does this even apply?!

Well, a photon is a prime example of a quanta. It is the absolute smallest value in which light may be measured!

Eureka! I get Quantum Mechanics!

Trust me; we've just begun :) Sorry, but i'm kind of confused.... 'Cause what else is new... Isn't visible light a part of the electromagnetic spectrum? If it is, then that means that light is made up of waves. How can light be made up of waves and particles? That's like a human, being awake and asleep at the same time! I thought that it wasn't possible! So you ARE paying attention! Well, Einstein's experiments caused much confusion. He thoroughly proved that light was indeed made up of particles, during his experiments. This challenged the claims of hundreds of physicists before him, who proved that light did indeed exist in a wave form. So then, how was the dispute solved? Who won - the particles side, or the waves side? Well, you see, they eventually came to a compromise. What was the compromise called, you may ask? It was called particle-wave duality. This concept suggested that light, depending on the experiment, could exist in either a particle OR light form. Similarly to how humans cannot be awake and sleeping simultaneously, light cannot exist in a particle and wave form simultaneously. Ahhh! I know, I know.....I was just wondering, though... Moving right along......Our next topic shall be: The Fabulous.... Emission Spectra! Taste the rainbow... If you look to the picture on your right, you'll see that an emission spectrum looks like a partially blacked-out rainbow. However, emission spectra are actually NOT rainbows. They are, in fact, one of the most useful ways in which to detect which elements make up an unidentified substance. Well, now that you mention it....they kind of do! Wait....but HOW? WELL.... When a substance is energized, it emits different forms of radiation (ex. infrared, gamma rays). Emission spectra show exactly how much of each kind of radiation and energized substance is emitting. Each element is unique in it's atomic composition, so each element subsequently has it's own distinct line spectrum. Line spectra show the radiative emissions of a substance at specific wavelengths. Therefore, it is possible to identify a 'mystery' substance by looking at it's emission spectrum, and matching it to the emission spectrum of an element. In the picture to the right, you can the the emission spectra of the elements Lithium, Sodium, Potassium, Rubidium, Cesium, Mercury, and Neon. OMYGOSH! PRETTY
COLOURS!!! Anyway, what's next? Actually, it's something pretty awesome.... Why do I get this terrible feeling every time you use the word awesome... MUAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA............... Quantum Numbers ......These numbers are used to determine the distribution, general location, and motion of electrons within an atom How many different quantum numbers are there? 4! The four different quantum numbers are: i) The Principal Quantum Number [n]
ii) The Angular Momentum Quantum Number [ ]
iii) The Magnetic Quantum Number [m ]
iv) The Electron Spin Quantum Number [m ] l l s The Principal Quantum Number [n] Can only have positive integral values (ie. n = 1, 2, 3, 4, ......) ....So, what does it tell us? The Principal Quantum Number tells us how far the electron is from the nucleus. The the value of n, the further away from the nucleus the electron is. As electrons move further away from the nucleus, they need more energy to stay in orbit, so conclusively, an in the value of n also leads to an in the value of energy needed to keep the electron in the orbital. The Angular Momentum Quantum Number [ ] l ....So, how do we find this number? Well, the Principal Quantum Number [n] is used to find the Angular Momentum Quantum Number [ ]. l l = n - 1 Formula: * note: if n=3, then you must solve the above formula for all the values that are equal to or less than n (ie. = 3 -1)
( = 2 - 1)
( = 1 - 1) l l l After calculating the value(s) of , assign them the following letters: This number divides electron shells into smaller groups of subshells [orbitals]. value of l l letter 0 s
1 p
2 d
3 f
4 g
5 h FYI: The 'S' subshells have the lowest energy out of all the subshells. The the value of , the the energy of the subshell! l The Magnetic Quantum Number [m ] l Tells us where the orbital is, in relation to space Using the value, we can figure out how many values of m there are, with the formula:
#m = 2 +1 l l l ie. if = 1, then there will be 3 values of m . l l *Note: How do we know what the actual numerical values of m are? Well... # of values of m numerical values 1 0 3 -1, 0, 1 5 -2, -1, 0, 1, 2 ...the m values tell us the number of orbitals within a subshell with an assigned value. l l l l The Electron Spin Quantum Number [m ] s Electromagnetic Theory - states that electrons behave like magnets because they are spinning, and it is the spinning motion that generates the magnetic field. WELL... We can't just IGNORE the spinning motion of the electrons.... = The creation of a NEW quantum number......the.... ELECTRON SPIN QUANTUM NUMBER ! This number [m ] = either 1/2 (clockwise spin) or -1/2 (counter-clockwise spin) l l Okay, so you know those "s,p,d,f" atomic orbitals? When do we even use them? THE ATOMIC ORBITALS ie. s, p, f, d OKay, so let's recap. Back in 'Quantum Numbers', we learned that the 2nd Quantum Number, the Angular Momentum Quantum Number [ ] helps us determine the 'shape' of the orbital [ie. s, p, f, d, g....] s Orbitals s orbitals are spherical in shape.
The diameter of the s orbital increases as the principal quantum number increases. Therefore, this idea of the s orbital reinforces the concept that the the principal quantum number, the further away from the nucleus the electron is located. p Orbitals p orbitals occur when the value of is greater than 0, therefore it starts with the principal number n=2 (ie. = n - 1, if n = 1, = 0) l l l *Note - there is 1 p orbital for every value of m . Therefore, for the principal quantum number n=2, there are 3 values of m , and subsequently 3 p orbitals, called 2p(x), 2p(y), and 2p(z).

The variable subscripts represent which axes each rotation is completed on, as show in the picture to the right. l l d Orbitals The lowest possible value of n for a d orbital is 3, because the value of must be equal to or greater than 3 in order to have any d orbitals. As there are 5 values of m for the n value of 3, there are 5 3d orbitals, show on the right. l l Electron Configuration Shows us how electrons are placed in the various orbitals EXAMPLE - The electron configuration for Hydrogen is: 1s^1 # of electrons in orbital/shell Angular Momentum Quantum Number [ ] l Principal Quantum Number [n] Pauli Exclusion Principle The Pauli Exclusion Principle is often used to determine the quantum numbers (specifically m ) of the electrons of atoms with more than one electron.

What it states - The Pauli Exclusion Principle states that it is impossible for two electrons in an atom to have 4 identical quantum numbers.

How it's used - From the principle, we can infer that only 2 electrons may inhabit the same orbital, and that those two electrons are spinning in different directions [ie. have different m values] s s Diamagnetism vs. Paramagnetism:
Diamagnetic substances are repelled by magnets as they do not contain electrons with unpaired spins. [ie. Hydrogen Atom]

Paramagnetic substances are attracted by magnets as they do contain electrons with unpaired spins. [ie. Lithium Atom] Shielding Effect The shielding Effect is when electrons in farther shells are protected from the attractive forces of the nucleus by the other shells between their's and the nucleus.

ie. Electrons in the p orbitals are 'shielded' from the attractive forces of the nucleus by the electrons in the s orbitals.

What is the EFFECT?
The effect is that, in the above scenario, the attraction between the protons of the nucleus and the electrons in the p orbitals are weakened. Hunds Rule What it states -
Arrangements of electrons with the most parallel spins [ ie. ] are the most stable arrangements of electrons. Aufbau Principle States that 1 electron is added to the orbitals every time 1 proton is added to the nucleus of am atom THE
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