The Structure of Atoms

Electromagnetic Radiation Made of two waves, one electric and one magnetic. Examples include light, microwaves, and radio signals. Wavelength (λ) is the distance between two crests. Units must be in meters (m) Frequency (ν) is the number of waves that pass a point per second. Units must be hertz (Hz)

Wavelength-Frequency Calculations c = the speed of light, and all electromagnetic radiation c = 2.998X108 m/s The frequency of radiation used in microwaves is 2.45 GHz. What is the wavelength?

Planck’s Equation Max Planck proposed that energy is quantized. The energy of a photons can only have certain values. E = hν h is Planck’s constant. h = 6.626X10-34 J•s Which has more energy? A mole of photons of orange light (λ = 625 nm) or a mole of photons of microwaves with a frequency of 2.45 GHz?

Line Emission Spectra Light is emitted when energy is supplied to atoms of an element. This is how neon lights work. If that light passes through a prism, it splits into a unique set of wavelengths for each element.

Line Emission Spectra for Different Elements

Assignment Page 297-298 2, 4, 5, 7, 10, 12, 14

Pages 297-302 2, 4, 5, 7, 10, 11, 13, 15, 19, 23, 25, 27, 34, 55, 59, 61, 68, 71, 73, 75, 77

Balmer Equation Use this equation to calculate the wavelength for the lines in the emission spectrum of hydrogen. 1 λ =𝑅( 1 2 2 − 1 𝑛 2 ) when n>2 R is the Rydberg constant. R = 1.0974X107 m-1 n is the principal quantum number. It tells us what energy level we are in. Calculate the wavelength for n = 4.

Niels Bohr Bohr proposed a model of the atom like planets orbiting around a star in a circular orbit. Bohr found an equation to calculate the energy of an electron in the nth orbit. 𝐸 𝑛 =− 𝑅ℎ𝑐 𝑛 2 If all the electrons in the atom are in their lowest energy levels, it is in the ground state. If the electrons are in a higher energy level, it is in an excited state.

Practice Calculate the energies for the n=1 and n=2 states for the hydrogen atom in joules per atom and kilojoules per mole.

The Lyman series includes all transitions ending at n=1. The Balmer series includes all transitions ending at n=2. The Paschen series includes all transitions ending at n=3. Red: n=3 to n=2 Green: n=4 to n=2 Blue: n=5 to n=2 Violet: n=6 to n=2

Energy For Emission Lines This equation will calculate the energy emitted in units of J/mol. ∆𝐸=− 𝑁 𝐴 𝑅ℎ𝑐( 1 𝑛 𝑓𝑖𝑛𝑎𝑙 2 − 1 𝑛 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 2 ) Calculate the change in energy and wavelength of the green line in Hydrogen’s line spectrum.

Practice Calculate the ionization energy for hydrogen. Ionization energy is the energy required to remove an electron from at atom. (n=1 to n=∞)

Wave-Particle Duality The photoelectric effect showed that light can behave like a particle as well as a wave. Does the same thing apply to matter? Louis de Broglie showed that is the case. Matter on a large scale doesn’t exhibit wave characteristics, but something as small as an electron does.

Finding the Wavelength for Matter de Broglie determined the following equation to calculate the wavelength of matter. λ= ℎ 𝑚𝑣 m is the mass and v is the velocity What is the wavelength of an electron with a mass of 9.109X10-31 kg traveling at 40.0% of the speed of light?

Heisenberg Uncertainty Principle In Bohr’s model, it is possible to know the location and energy for an electron, but that isn’t true for the current model. The uncertainty principle says that you can’t accurately know both the position and energy for an electron. If you accurately measure the energy, the position has a large uncertainty. This introduces the idea that an electron has a probability of being in a particular location. Werner Heisenberg

Quantum Mechanics Erwin Schrödinger explained the behavior of electrons in what is now called quantum mechanics. He used wave functions to explain the behavior. Electrons are standing waves. This means electrons are quantized. The wave function gives the amplitude of the wave. The square of the wave function gives the probability of finding the electron. The energy of the electron is known precisely, so we discuss the probability of finding the electron. Orbitals (s,p,d,f) describe the region where an electron is most likely located.

Quantum Numbers Principal Quantum Number: n = 1, 2, 3, 4,… Tells us the energy and size of the orbital Azimuthal Quantum Number: l = 0, 1, 2,…,n-1 In each shell, there are subshells represented by letters l = 0 is s, l = 1 is p, l = 2 is d, and l = 3 is f. Magnetic Quantum Number: ml = 0, ±1, ±2, ±3,…, ±l Related to the orientation of the orbital If n=1, what values are possible for l and ml. What if n=3?

Interesting Facts about Quantum Numbers n = the number of subshells in a shell 2l+1 = the number of orbitals in a subshell n2 = the number of orbitals in a shell

Nodal Planes The number of nodal planes has a pattern for each shape of orbital. s has no nodal planes, p has one, d has two and f has three. A nodal plane goes through the nucleus and goes through a node, an area with no probability of finding an electron.

Spin There is a fourth quantum number called the Spin Quantum Number. ms can have a value of +1/2 and -1/2. Since electrons are charged, the produce a magnetic field when they move.

Diamagnetic and Paramagnetic Each orbital can hold two electrons. It is possible to have all of the electrons paired up, or some can be unpaired. If a substance has all of the electrons paired, it is diamagnetic. As a result, it will not be affected by a magnetic field. If a substance has unpaired electrons, it is paramagnetic. As a result it will be affected by a magnetic field.