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Neils Bohr
Different wavelengths of light are “bent” or refracted at different angles when they enter and leave the glass. This separates the different wavelengths, making them visible to the naked eye.
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Introduction to Quantum Mechanics
"I think it is safe to say that no one understands quantum mechanics." – Physicist Richard P. Feynman
Neils Bohr (1885 – 1962) Neils Bohr came to the Cavendish laboratory, headed by Ernest Rutherford in 1912. He had decided to investigate the structure of the atom, but instead of using radiation like Rutherford, he was intrigued by earlier work with a technique known as spectroscopy. Spectroscopy was used to observe the unique pattern of spectral lines produced by elements. When a solid mass, such as iron, is heated strongly, it radiates a range of electromagnetic waves. This includes visible light, which we can observe, and infrared light, which we can feel as heat. However, when a gas is heated, it only emits electromagnetic waves with very specific frequencies. If the light from a gas discharge tube containing the vapour of an element is passed through a prism, the individual electromagnetic waves it emits can be observed as lines. These are called spectral lines. The lines observed are unique to the vaporous element, like a fingerprint. In fact, the element helium was discovered this way by looking at the sun. For a long time, helium was thought to only exist in the sun (in fact, the name helium means “of the sun”). Bohr sought an explanation for spectral lines. He used Max Plänck’s idea that energy is quantized to suggest that if light comes in discrete quanta, then perhaps electrons are also only “allowed” certain energy levels.
Figure 1. Set-‐up for Observing Bright-‐line Spectra
The idea that electrons can only exist at specific energy levels allowed Bohr to explain the spectral lines as the energy emitted by electrons when they move from a high energy level to a lower one. From this idea, it followed that atoms only emit photons with energies equivalent to the differences between energy levels.
Bohr’s First Postulate The orbits of electrons are stationary states. Electrons do not emit energy in these stationary states. Bohr’s Second Postulate Electrons can only gain or lose energy by making a transition between different stationary states.
An atom in its ground state. Its electron encounters a source of energy.
The electron transitions to a higher energy level. The atom is now in an excited state.
The electron returns to a lower energy level and emits a photon of energy equal to the transition of the electron.
To summarize, when electrons encounter a source of energy, such as high energy photons, they provide the energy to for the electron to make a transition to a higher energy level. However this state is unstable, and electrons quickly return to their former energy levels. When electrons fall back to their original stationary state, they emit a photon of energy equal to the energy required to make the transition. This is what results in spectra lines. Although Bohr described electrons as ‘orbits’, physically that is not what is meant. Orbits are a symbol for the energy states of electrons. Erwin Schrödinger (1887 – 1961) Using the idea of electrons as waves, Erwin Schrödinger developed a set of mathematical equations that treated electrons as waves. He assigned electrons a waveform function, ϕ. Schrödinger’s equations defined a region space around which an electron is most like found. This gives a definite shape to orbitals, defined by the volume around the nucleus the electron in a particular orbital is most likely found. The development of these equations was the one of the earliest formulations of Quantum mechanics. In this sense, the orbital can be thought of as an electron cloud. This cloud that surrounds the nucleus is a probability map of where electrons are most likely found, with the opacity of the cloud proportional to the probability density. I.e. the denser the cloud, the more likely an electron will be found there. Orbitals can thus be viewed as a 3D electron probability density map that outlines the area the electron is probably found. Werner Heisenberg (1901 – 1976) Simultaneous to Schrödinger, Werner Heisenberg also developed a set of equations that explained the behaviour of electrons. However, the math was so complicated, that Heisenberg himself did not fully understand why it explained the quantum nature of electrons. Nonetheless, Heisenberg and Schrödinger’s discoveries gave birth to quantum mechanics.
I knew of [Heisenberg's] theory, of course, but I felt discouraged, not to say repelled, by the methods of transcendental algebra, which appeared
difficult to me, and by the lack of visualizability.
-Schrödinger in 1926
One of the consequences of quantum mechanics is that it is not possible to simultaneously know the position and momentum (speed and direction) of a particle. This was determined by Heisenberg, and is hence called the Heisenberg Uncertainty Principle. Imagine you are trying to determine the speed and position of a runner in a race. To do this, you might use a laser device and timer to measure the distance to the runner and how fast they are traveling. This is very
similar to how police determine the speed of cars using radar guns. The device fires photons at the object. The photons are reflected off the object and back to the observer. The time it takes for the photons to return can be used to determine the speed and position of the runner. Now imagine you are trying to determine the speed and position of an electron around a nucleus. If you use the same methods as for the runner or the car, you fire a photon at the electron. However, the big difference here is that the electron is quite a bit smaller than the runner. When the photons strike the runner, their effect on the runner’s position/speed is negligible. However, for the electron, the photon can have a large effect on the motion of the electron. This makes your observation of the electron’s motion very uncertain. Basically, the smaller the system you are trying to observe, the more uncertain any measurements you make on that system will be. Structure & Bonding – Electron Orbitals, Quantum Numbers Bohr’s model of the atom did not correctly predict the correct spectral lines for elements other than hydrogen. Following Bohr’s contributions, other scientists continued research into spectral lines, which further improved our understanding of the electron structure of atoms. The system used today describes each electron in an atom using four numbers. This is similar to your address. For example, you might use four values to describe where you live: province, city, street, number. The numbers used to describe electrons in an atom are called quantum numbers. Orbitals An orbital is a region of space around the nucleus of an atom that an electron may be found in. Although the word orbital is derived from the word ‘orbit’, this is not meant to imply that electrons move in an orbit-‐like path around the nucleus. They do not!
Principal Quantum Number, n The principal quantum number describes the stationary state, or energy shell an electron is found in. This also describes how far the electron is from the nucleus of the atom. Therefore, the larger the value of n, the larger the orbital will be.
Energy Level Diagrams • Now when we draw energy level diagrams, we must include:
o the sublevels of each shell o the spin of each electron
• When creating energy level diagrams for elements, there are two important rules we must obey: o Pauli’s Exclusion Principle
§ No two electrons may have the same set of quantum numbers. o Hund’s Rule
§ One electron must occupy each orbital of the same energy level before a second electron occupies an orbital.
• When adding electrons in electron configurations, we can use the Aufbau principle to help us (aufbau = “building up”). (see diagram on next page)
Rules for Anions • Add the extra electrons corresponding to the ion charge to the total number of electrons before
distributing electrons in orbitals. Rules for Cations • Create the energy-‐level diagram for the neutral atom first, then remove the number of electrons
equivalent to the charge from the orbital with the highest principle quantum number first.
Energy Level Diagram
4n
3n
2n
1n
Every orbital can hold 2 electrons with opposite spin. Indicate electrons with arrows:
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