Electronic Structure of Atoms Ch 6

The wavelength of a wave.

3 Characteristics of Electromagnetic Radiation Wavelength (l - lamda) distance between 2 consecutive peaks measured in meters Frequency (n - nu) the number of waves per second that pass a given point in space measured in 1/s or hertz Speed (c) all electromagnetic radiation travels at the same speed. 2.998 x 108 m/s = approximately 3 x 108 m/s c = n l

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FM Radio broadcasts at 88 to 108 megahertz FM Radio broadcasts at 88 to 108 megahertz. An FM radio station broadcasts at a frequency of 91.5 megahertz. What is it’s wavelength? AM Radio broadcasts at 500 – 1600 kilohertz. KDLM broadcasts at 1340 Kh or 1,340,000 hertz. What is the wavelength?

3 Observations Blackbody radiation is the emission of light from a hot object. Photoelectric effect is the emission of e- from a metal surface on which light is shining. Spectra emission is light from electronically excited gaseous atoms.

Quantum Theory - Max Planck found that energy could only be gained or lost in whole number quantities. DE = h n DE = change in energy (joules) h = Planck’s constant 6.626 x 10-34 joule second or 6.626 x 10-34 Kg m2/s n = frequency in 1/s or hertz It had been thought that Energy was continuous. We now know that it is quantized, in discrete units called quantum. Albert Einstein purposed the idea all electromagnetic radiation is quantized in streams of particles called photons.

For electromagnetic radiation of wavelength 242 For electromagnetic radiation of wavelength 242.4 nm, which is the longest wavelength that will bring about the photo dissociation of O2 , the photoelectric effect. What is the energy of one photon? Of 1 mole of photons?

The dual nature of light Wave evidence Reflection as in a mirror Refraction: the bending of light as it passes into a new medium with a different index of diffraction. Diffraction: the spreading out of light into the different wavelengths of light (different colors of the rainbow) Particle evidence light exerts pressure Photoelectric is the emission of e- from a metal surface on which light is shining Black body radiation is the emission of light from a hot object. Spectra emissions is light from electronically excited gaseous atoms.

Bohr’s model – The Quantum model of the Atom The e- in the hydrogen atom move around the nucleus only in certain allowed circular orbits. e- move in a circular orbit 2. e- has only a fixed set of orbitals. As long as an e- remains in a fixed orbital, it’s energy is constant. 3. e- can pass only from 1 allowed orbital to another. Discrete quantities of energy.

When an e- gains energy, it will jump to a higher energy level (excited). They will always come down to the ground state (lowest possible energy state or level available) The energy difference between the two energy levels will be given off as light. Colors and wavelengths of photons in the visible region. Hydrogen bright line spectra.

An excited H atom returns to a lower energy level.

DE = Eenergy of final state – E energy of initial state. EN = -2 DE = Eenergy of final state – E energy of initial state EN = -2.179 x 10-18 J EN = energy of specific energy level N = energy level N2 Determine the wavelength of the light emitted from a hydrogen atom when an e- drops from the 5th energy level to the 2nd energy level.

The color of the photon emitted depends on the energy change that produces it.

De Broglie’s equation is used to determine the mass of a particle traveling as a wave. l = h / mv l = wavelength in m h = Planck’s constant 6.626 x 10-34 Kg m2/s m = mass in Kg v = velocity in m/s

What is the wavelength associated with an e- traveling 1/10 the speed of light? me- = 9.10 x 10-31 Kg

Heisenberg’s Uncertainty Principle X – D ( m n ) > h/ 4p X = position uncertainty m n = momentum uncertainty There is a fundamental uncertainty as to the position and momentum of an e- at any given time. The more accurate we know the position, the less we know about the momentum.

Bohr’s model works for the hydrogen atom, but it became apparent quickly that it would not work for more complex atoms. Heisenberg, de Broglie, and Schrodinger used wave mechanics or quantum mechanics to approach the structure of the atom. They showed that e- act as a particle and a wave. They thought of the e- as a standing wave, as in musical instruments. Schrodinger worked out the math to explain the e- wave function y (psi) = orbital

We know the probability of e- in a region y2 The orbital that describes the e- density of the hydrogen electron in its lowest possible energy state.

Quantum Numbers : define position of the e- in the atom Principle quantum number (n) = energy level integral value = 1, 2, 3, … Angular Momentum quantum number (l) = sublevel or the shape of the orbitals integral value of 0 to n-1 l = 0  s sublevel l = 1  p sublevel l = 2  d sublevel l = 3  f sublevel

Magnetic quantum number (ml ) = orbital. integral value = - l to + l Magnetic quantum number (ml ) = orbital integral value = - l to + l l = 0  s sublevel  ml = 0 l = 1  p sublevel  ml = -1, 0, +1 l = 2  d sublevel  ml = -2, -1, 0, +1, +2 l = 3  f sublevel  ml = Electron Spin quantum number (ms) = the 2 e- in an orbital will spin the opposite direction. Value of +1/2 or -1/2

Charts show the radii probability Charts show the radii probability. This shows the distance that e- are most likely found from the nucleus.

The hydrogen 1s orbital. The 1s orbital is a sphere that encloses 90% of the total e- probability.

Relative sizes of the spherical 1s, 2s, and 3s orbitals of hydrogen.

The three 2p orbitals.

Diagram of principal energy levels 1 and 2.

Rules for assigning the principle quantum numbers. 1. e- occupy the orbitals in a way to minimize the energy of the atom. 2. No 2 e- have all 4 quantum numbers the same (Pauli Exclusion Principle) 3. e- will occupy the lowest energy configuration available. When orbitals of identical energy are available, e- occupy these orbitals singly (Hund’s rule). Atoms tend to have as many unpaired e- as possible. Aufbau principle: As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to these hydrogen – like orbitals.

Unusual configurations Expect to see What actually occurs Cr: [Ar] 4s2 3d4 Cr: [Ar] 4s1 3d5 Cu: [Ar] 4s2 3d9 Cu: [Ar] 4s1 3d10

1. Helium 4s 3px 3py 3pz 3s 2px 2py 2pz Electron configuration ___________________________________ 2s 1s Core notation ____________________________________

2. Nitrogen 4px 4py 4pz 3d 3d 3d 3d 3d 4s 3px 3py 3pz 3s 2px 2py 2pz Electron configuration _______________________________________ 2s 1s Core notation _____________________________________________

Orbitals being filled for elements in various parts of the periodic table.

Filling order for placement of e- in the orbitals. 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p Filling order for placement of e- in the orbitals.