The Atom Chem Honors

Atoms Atoms are so small that they are difficult to study Atomic models are constructed to explain experimental data on collection of atoms. Scientific models of the atom had to be constantly revised to fit new data

Dalton’s Atomic Theory Dalton theorized that Atoms…. Are tiny particles of matter too small to see Are able to combine with other atoms to make compounds Each element has similar physical and chemical properties and different elements have different physical and chemical properties And a chemical reaction is the rearrangement of atoms

Subatomic Particles Electrons – J.J. Thompson was investigating electric discharge when he first discovered the electron. An amazing glow could be observed when a high voltage was a applied a gas volume at low pressures. The glow was caused by something coming from the cathode (the negatively charged pole). Thompson observed that the cathode ray interacted with both an electric field and a magnetic field – so the species must be electrically charged. Thompson ran several experiments measuring how the cathode ray was deflected by both the magnetic and electric field – Thompson was able to determine the mass to charge ratio of the elementary particle. (mass was found to be 1/1837 of a H atom)

The Electron

Subatomic Particles Protons - Atoms were known to be neutral, so with the discovery of the electron, a search for the positively charged particle in an atom occurred Goldstein discovered the proton by using a discharge tube containing a perforated cathode. He found that some rays pass in a direction opposite of the cathode rays. These are also know as anode rays as they are coming from a perforated anode.

Subatomic Particles Neutrons – After bombarding a beryllium atom with alpha particles (2 neutrons, 2 protons), Rutherford noticed an emission of radiation The radiation was highly penetrating The radiation was unaffected by an electric or magnetic field It was found to have approximately the same mass as the protons

Rutherford’s Atom Rutherford originally proposed that the atom looked like plum pudding The plum pudding model proposed that the atom was a cloud of positive charge (protons) with negatively charged particles (electrons) spread uniformly throughout the atom

Rutherford’s Gold Foil Experiment

Rutherford’s Gold Foil Experiment

Rutherford’s Atomic Structure The atom must have a densely packed nucleus that contains all of the mass of the atom The nucleus must contain the protons Rutherford proposed that the electrons must revolve around the nucleus of the atom much like how the planets in our solar system orbit the sun.

Atomic Spectroscopy and the Bohr Model Another mystery in the early twentieth century involved the emission spectra observed from energy emitted by atoms and molecules.

Continuous vs. Line Spectra For atoms and molecules, one does not observe a continuous spectrum (the “rainbow”), as one gets from a white light source. Only a line spectrum of discrete wavelengths is observed. Each element has a unique line spectrum.

Bohr’s Model of the Atom If the atom behaved in a classical manner, the orbited electrons would spiral into the positively charged nucleus As the electron spiraled it would release energy in a continuous fashion and would cause a continuous atomic emission spectrum (like white light) More importantly the atom would not be stable!!! In order to explain the atomic emission spectrum, Bohr utilized information collected from Planck’s (Blackbody radiation) and Einstein’s (Photoelectron effect) experiments. He deduced that the atom must be quantized and electrons must only resides at discrete energy levels

The Hydrogen Spectrum Johann Balmer (1885) discovered a simple formula relating the four lines to integers. Johannes Rydberg advanced this formula.

Wave-Particle Duality Earlier we discussed how light can behave like a wave and also like a particle Light: Double Slit Experiment – Light behaved like a wave when placed through a narrow slit and was diffracted. When two slits were introduced the diffracting light waves could constructively and destructively interfere with each other and form an interference pattern on the detector. Photoelectron Effect – It was observed that you could bombard a metal surface with a large amount of high intensity light , but if the individual photons are low energy, no photoelectrons will be emitted. It shows that the light is delivered in specific, discrete amounts, as if a “particle” collided with the surface.

Wave/Particle Duality If light can behave like a wave or a particle, can matter behave like a wave?

The Wave Nature of Matter Louis de Broglie theorized that if light can have material properties, matter should exhibit wave properties. He demonstrated that the relationship between mass and wavelength was The wave nature of light is used to produce this electron micrograph.  = h m

The Wave Nature of Matter An electron moving about the nucleus of an atom behaves like a wave and therefore has a wavelength. Matter waves must then have a momentum (mv) However the wavelength associated with an object of ordinary size is so small it is completely unobservable.  = h mv

Checkpoint What is the wavelength of an electron moving with a speed of 5.97 x 106 m/s? The mass of an electron is 9.11 x 10-31kg. (Planck’s constant – 6.626 x 10-34 m2 kg/ s)

Double Slit Experiment

Double Slit (Observation of the electron)

The Uncertainty Principle Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position is known: (x) (mv) ≥ h 4π

Indeterminacy In classical physics, we can determine the trajectory of a object in motion based of its original position and its velocity (we also have to determine the forces acting on it.) If we can not know the position and the velocity of an electron – we can not know its trajectory Probability Distribution Map – statistical map that shows where an electron is likely to be found under a given set of conditions

The Classical Concept of Trajectory

Probability Distribution

Quantum Mechanics Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. This is known as quantum mechanics.

Quantum Mechanics The solution of Schrödinger’s wave equation is designated with a lowercase Greek psi (). The square of the wave equation, 2, gives the electron density, or probability of where an electron is likely to be at any given time.

Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. Each orbital describes a spatial distribution of electron density. An orbital is described by a set of three quantum numbers.

Principal Quantum Number (n) The principal quantum number, n, describes the energy level on which the orbital resides. The values of n are integers ≥ 1. These correspond to the values in the Bohr model.

Angular Momentum Quantum Number (l) This quantum number defines the shape of the orbital. Allowed values of l are integers ranging from 0 to n − 1. We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

Angular Momentum Quantum Number (l)

Magnetic Quantum Number (ml) The magnetic quantum number describes the three-dimensional orientation of the orbital. Allowed values of ml are integers ranging from −l to l: −l ≤ ml ≤ l Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, and so forth.

Magnetic Quantum Number (ml) Orbitals with the same value of n form an electron shell. Different orbital types within a shell are subshells.

Checkpoint (a) Predict the number of subshells in the fourth shell, that is, for n =4. (b) Give the label for each of these subshells. (c) How many orbitals are in each of these subshells?

s Orbitals The value of l for s orbitals is 0. They are spherical in shape. The radius of the sphere increases with the value of n.

s Orbitals For an ns orbital, the number of peaks is n. For an ns orbital, the number of nodes (where there is zero probability of finding an electron) is n – 1. As n increases, the electron density is more spread out and there is a greater probability of finding an electron further from the nucleus.

p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them.

d Orbitals The value of l for a d orbital is 2. Four of the five d orbitals have four lobes; the other resembles a p orbital with a doughnut around the center.

f Orbitals Very complicated shapes Seven equivalent orbitals in a sublevel l = 3

Energies of Orbitals—Many-electron Atoms As the number of electrons increases, so does the repulsion between them. Therefore, in atoms with more than one electron, not all orbitals on the same energy level are degenerate. Orbital sets in the same sublevel are still degenerate. Energy levels start to overlap in energy (e.g., 4s is lower in energy than 3d.)

Spin Quantum Number, ms In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. The “spin” of an electron describes its magnetic field, which affects its energy. This led to the spin quantum number, ms. The spin quantum number has only two allowed values, +½ and –½.