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Alright class we are going back to quantum numbers.

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## Alright class we are going back to quantum numbers.

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**Alright class we are going back to quantum numbers.**I decided this would be a better lead into dipole then just throwing you into the mess.**Do you remember Wave and Frequency?**• Do you remember plank. Well he is back it is time to work on his constant and what it means. • Also the electromagnetic spectrum.**Properties of Waves**Wavelength (l) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. Frequency (n) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = l x n 3**Maxwell (1873), proposed that visible light consists of**electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 108 m/s All electromagnetic radiation l x n = c 4**A photon has a frequency of 6.0 x 104 Hz. Convert this**frequency into wavelength (nm). Does this frequency fall in the visible region? 6**The wavelength of the green light from a traffic signal is**centered at 522 nm. What is the frequency of this radiation? 7**Problem 1**What is the wavelength (in meters) of an electromagnetic wave whose frequency is 3.64 x 107 Hz? 8**Mystery #1, “Heated Solids Problem”Solved by Planck in**1900 When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths. Radiant energy emitted by an object at a certain temperature depends on its wavelength. Energy (light) is emitted or absorbed in discrete units (quantum). E = h x n Planck’s constant (h) h = 6.63 x 10-34 J•s 9**Calculate the energy (in joules) of a photons with a**wavelength of 5.00 x 104 nm (infrared region). 10**Calculate the energy (in joules) of a photons with a**wavelength of 5.00 x 10-2 nm (x-ray region). 11**Problem 2**The energy of a photon is 5.87 x 10-20 J. What is its wavelength in nanometers? 12**Mystery #2, “Photoelectric Effect”Solved by Einstein in**1905 hn • Light has both: • wave nature • particle nature KE e- Photon is a “particle” of light hn = KE + W KE = hn - W where W is the work function and depends how strongly electrons are held in the metal 13**When copper is bombarded with high-energy electrons, X rays**are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is 0.154 nm. 14**The work function of cesium metal is 3.42 x 10-19 J.**Calculate the minimum frequency of light necessary to eject electrons from the metal. 15**The work function of cesium metal is 3.42 x 10-19 J.**Calculate the kinetic energy of the ejected electron if light of frequency 1.00 x 1015 s-1 is used for irradiating the metal. 16**Problem 3**The work function of titanium metal is 6.93 x 10-19 J. Calculate the energy of the ejected electrons if light of frequency 2.50 x 1015 s-1 is used to irradiate the metal. KE = _____x 10-19 J 17**Line Emission Spectrum of Hydrogen Atoms**Mystery #3, “Emission Spectra” 18**( )**En = -RH 1 n2 Bohr’s Model of the Atom (1913) • e- can only have specific (quantized) energy values • light is emitted as e- moves from one energy level to a lower energy level n (principal quantum number) = 1,2,3,… RH (Rydberg constant) = 2.18 x 10-18J 20**E = hn**E = hn 21**ni = 3**ni = 3 f i ni = 2 nf = 2 DE = RH i f ( ) ( ) ( ) Ef = -RH Ei = -RH nf = 1 nf = 1 1 1 1 1 n2 n2 n2 n2 Ephoton = DE = Ef - Ei 22**Calculate the wavelength (in nm) of a photon emitted by a**hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. 24**Problem 4**What is the wavelength (in nm) of a photon emitted during a transition from ni=6 to nf=4 in the H atom? ν = _____x 103 nm 25**h**2pr = nll = mu Why is e- energy quantized? De Broglie (1924) reasoned that e- is both particle and wave. u = velocity of e- m = mass of e- 26**What is the de Broglie wavelength (in nm) associated with a**2.5 g Ping-Pong ball traveling at 15.6 m/s? 27**Calculate the wavelength of the ‘particle’ in each of**the following two cases: (a) The fastest serve ever recorded in tennis was about 150 miles per hour, or 68 m/s. Calculate the wavelength associated with a 6.0 x 10-2 kg tennis ball travelling at this speed. 28**Calculate the wavelength of the ‘particle’ in each of**the following two cases: (b) Calculate the wavelength associated with an electron (9.1094 x 10-31kg) travelling at this speed. 29**Problem 5**Calculate the wavelength (in nm) of a H atom (mass = 1.674 x 10-27 kg) moving at 7.00 x 102 cm/s. 30**Chemistry in Action: Laser – The Splendid Light**Light Amplification by Stimulated Emission of Radiation Laser light is (1) intense, (2) monoenergetic, and (3) coherent 31**Chemistry in Action: Electron Microscopy**le = 0.004 nm STM image of iron atoms on copper surface Electron micrograph of a normal red blood cell and a sickled red blood cell from the same person 32**Shortcomings of Bohr’s model**• Did not account for the emission spectra of atoms containing more than on electron. • Did not explain extra lines in the emission spectra for hydrogen when magnetic field is applied. • Conflict with discovery of ‘wavelike’ properties – how can you define the location of a wave? Heisenberg Uncertainty Principle It is impossible to know simultaneously both the momentum p (defined as mass times velocity) and the position of a particle with certainty. 33**Schrodinger Wave Equation**In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e- 34**Schrodinger Wave Equation**• Wave function (y) describes: • . energy of e- with a given y • . probability of finding e- in a volume of space • Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems. 35**Schrodinger Wave Equation**n=1 n=2 n=3 y is a function of four numbers called quantum numbers (n, l, ml, ms) principal quantum number n n = 1, 2, 3, 4, …. distance of e- from the nucleus 36**Where 90% of the**e- density is found for the 1s orbital 37**Schrodinger Wave Equation**quantum numbers:(n, l, ml, ms) angular momentum quantum number l for a given value of n, l= 0, 1, 2, 3, … n-1 l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e- occupies 38**l = 1 (p orbitals)**l = 0 (s orbitals) 39**Schrodinger Wave Equation**quantum numbers: (n, l, ml, ms) magnetic quantum number ml for a given value of l ml = -l, …., 0, …. +l if l = 1 (p orbital), ml = -1, 0, or1 if l = 2 (d orbital), ml = -2, -1, 0, 1, or2 orientation of the orbital in space 41**3 orientations is space**ml = -1, 0, or1 42**ml = -2, -1, 0, 1, or2**5 orientations is space 43**Schrodinger Wave Equation**(n, l, ml, ms) spin quantum number ms ms = +½or -½ ms = +½ ms = -½ 44**Schrodinger Wave Equation**quantum numbers:(n, l, ml, ms) Existence (and energy) of electron in atom is described by its unique wave function y. Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time 45**Schrodinger Wave Equation**quantum numbers:(n, l, ml, ms) Shell – electrons with the same value of n Subshell – electrons with the same values of nandl Orbital – electrons with the same values of n, l, andml How many electrons can an orbital hold? 47**How many 2p orbitals are there in an atom?**How many electrons can be placed in the 3d subshell? 48**List the values of n, ℓ, and mℓ for orbitals in the 4d**subshell. What is the total number of orbitals associated with the principle quantum number n=3? 49**Problem 6**Give the values of the quantum numbers associated with the orbitals in the 3p subshell. n = ____ ℓ = ____ mℓ=____ 50