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Home , Atomic orbital, Lyman series, Magnetic quantum number

Atomic Structure and the The electronic structure of an determines its characteristics Studying by analyzing light emissions/absorptions

: analysis of light emitted or absorbed from a sample  Instrument used = spectrometer  Light passes through a slit to become a narrow beam  Beam is separated into different colors using a prism (or other device)  Individual colors are recorded as spectral lines Electromagnetic radiation

 Light  A of electric and magnetic fields  Speed = 3.0 x 108 m/s  () = distance between adjacent peaks  Unit = any length unit  Frequency () = number of cycles per second  Unit = hertz (Hz) Relationship between properties of EM

 Wavelength x frequency = speed of light

·v = c Calculate the frequency of light that has a wavelength of 6.0 x 107 m.

Calculate the wavelength of light that has a frequency of 3.7 x 1014 s-1 Visible Light

from 700 nm (red) to 400 nm (violet)  No other wavelengths are visible to humans Quanta and

 Quanta: discrete  Analogy: Water flow amounts  Energy is quantized – restricted to discrete values  Only mechanics can explain behavior Another analogy for quanta

A person walking up steps – his potential energy increases in a quantized manner Photons

 Packets of  electromagnetic energy -34  Travel in waves h = 6.63 x 10 Js  Brighter light = more photons passing a point per second  Higher energy photons E = hv have a higher frequency of radiation The energy of a is directly proportional to its frequency Deriving Planck’s constant

In a laboratory, the energy of a photon of blue light with a frequency of 6.4 x 1014 Hz was measured to have an energy of 4.2 x 1019 J.

Use Planck’s constant to show this: E = (6.63 x 10-34 J·s) x (6.4 x 1014 1/s) = 4.2 x 1019 J Evidence for photons

– the ejection of from a when exposed to EM radiation  Each substance has its own “threshold” frequency of light needed to eject electrons

Determining the energy of a photon

 Use Planck’s constant!  What is the energy of a E = hv photon of radiation with a frequency of 5.2 x 1014 waves per second? Another problem involving photon energy

 What is the energy of a photon of radiation with a wavelength of 486 nm? – proposed that matter and radiation have properties of both waves and (Nobel Prize 1929)

 Calculate the wavelength of a atom  = h moving at 7.00 x 102 cm/sec m

m = mass h = Planck’s constant

 = velocity Hydrogen spectral lines

Balmer series:

n1 = 2 and n2 = 3, 4, …

Lyman series (UV lines):

n1 = 1 and n2 = 2, 3, …

Atomic Spectra and Energy Levels

 Johann Balmer – noticed that the lines in the visible  Observe the hydrogen region of hydrogen’s gas tube, use the prism to spectrum fit this see the frequencies of EM expression: radiation emitted

v= (3.29 x 1015 Hz) x 1 - 1 4 n2

n = 3, 4, … Rydberg equation: works for all lines in hydrogen’s spectrum v= R x 1 - 1 H 2 2 n1 n2

15 -1 RH = 3.29 x 10 s

Rydberg Constant Energy associated with electrons in each principal

Energy of an electron in a -18 E = -2.178 x 10 joule n2

n = principal Differences in Energy Levels of the hydrogen atom

Use the Rydberg Equation OR Use the expression for each energy level’s energy in the following equation:

E = Efinal – Einitial ’s contribution

 Assumed e- move in circular orbits about the nucleus  Only certain orbits of definite are permitted  An electron in a specific orbit has a specific energy that keeps it from spiraling into the nucleus  Energy is emitted or absorbed ONLY as the electron changes from one energy level to another – this energy is emitted or absorbed as a photon

Summary of spectral lines

 When an e- makes a transition from one energy level to another, the difference in energy is carried away by a photon  Different excited hydrogen atoms undergo different energy transitions and contribute to different spectral lines The –

 The dual of matter limits how precisely we can simultaneously measure location and momentum of small particles  It is IMPOSSIBLE to know both the location and momentum at the same time Atomic Orbitals – more than just principal energy levels

 Erwin Schrodinger (Austrian)  Calculated the shape of the wave associated with any  Schrodinger equation – found mathematical expressions for the shapes of the waves, called wavefunctions (psi)  Born’s contribution

(German)  The of finding the electron in space is proportional to 2 Called the “probability  density” or “” – the wavefunction for an electron in an atom

 s – high probability of e- being near or at nucleus

ELECTRON IS NEVER AT THE NUCLEUS IN THE FOLLOWING ORBITALS:  p – 2 lobes separated by a nodal plane  d – clover shaped  f – flower shaped

More about orbitals

Each orbital can hold 2 electrons Orbitals in the same subshell have equal energies Quantum numbers – like an “address” for an electron n =  As n increases, orbitals become larger  Electron is farther from nucleus more often higher in energy less tightly bound to nucleus

Quantum numbers

 l = quantum number  Values: 0 to n – 1  Defines the shape of the orbital

Value of l 0 1 2 3 Letter s p d f used Quantum numbers

ml = the  Orientation of orbital in space

(i.e. px py or pz)  Values: between – l and l, including 0

Example: for d orbitals, m can be -2, -1, 0, 1, or 2 For p orbitals, m can be -1, 0, or 1 Quantum numbers

 ms = the number  When looking at line spectra, scientists noticed that each line was really a closely-spaced pair of lines!  Why? Each electron has a SPIN – it behaves as if it were a tiny sphere spinning upon its own axis  Spin can be + ½ or -1/2  Each represents the direction of the magnetic field the electron creates Describe the electron that has the following quantum numbers:

n = 4, l = 1, ml = -1, ms = +1/2

Principal level 4 4p orbital

px orbital spin up Are these sets of quantum numbers valid?

3, 2, 0, -1/2 2, 2, 0, 1/2

Electron configuration: rules

1. – electrons fill lowest energy levels first 2. Pauli exclusion principle – only 2 electrons may occupy each orbital 3. Hund’s rule – electrons spread out over orbitals of equal energy before doubling up Special rules

 One electron can move from an s orbital to the d orbital that is closest in energy  Only happens to create half or whole-filled d orbitals  Examples: Cr, Cu Configuration

 A shorter electron  Examples: configuration  Cl  Write the symbol for the noble gas BEFORE the element in brackets  Write the remainder of  Cs the configuration Energy level specifics

 s and d orbitals are close 4s in energy  Example  4s electrons have slightly lower energy than 3d electrons  The s electrons can penetrate to get closer to the nucleus, giving them slightly lower energy

3d