Atomic Physics m 10529 0 10202 nanrneV6 132nEn Atom Nucleus electrons Nucleus Proton s neutron s hydrogen only one proton Proton Two up quarks and one down quark Neutron One up quark and two down quarks Quark Are these obvious Of course not Take a piece of wood what happens if we keep cutting it It is likely that you cannot keep cutting forever There should exist smallest units atoms Atom Greek atomos a not tomos cutting John Dalton 09 06 1766 07 27 1844 Pioneering work in the development of modern atomic theory of chemistry J J Thomson s Discovered electron in 1897 Atoms can actually be divided Thomson proposed a model of the atom A volume of positive charge Electrons embedded throughout the volume like seeds in a watermelon Watermelon model of atom Experiment Rutherford and his students 1911 Source alpha particles later identified as helium nucleus Much heavier than electrons Most of the alpha particles passed though the thin metal foil A few deflected significantly from their original paths Some even reversed their direction of travel Rutherford 1911 Planetary model Positive charge and most of the mass of an atom is concentrated at the center of the atom called the nucleus Electrons orbit the nucleus like planets orbit the sun The atoms is mostly EMPTY and so we our body are mostly empty Unfortunately this model encountered serious difficulties in explaining atomic spectra The Rutherford model was not able to explain characteristic emission absorption lines In Rutherford s model electrons are undergoing a centripetal acceleration and so should radiate electromagnetic waves of the same frequency The radius should steadily decrease as this radiation is given off because electron continues to give out energy The electron should eventually spiral into the nucleus All atoms should collapse not stable NOT true An atom can emit light at specific wavelengths An atom can also absorb light at specific wavelengths The positions of absorption lines coincide with the bright lines of the emission spectrum Emission absorption spectra can be used to identify elements fingerprint of elements Lyman series Balmer series Paschen series ultraviolet visible infrared In1888 Rydberg came up with a formula that can calculate ALL emission lines of hydrogen atom Where does this crazy constant come from RH is the Rydbergconstant 1 097 x 107 m 1 However Rydberg was not able to provide an explanation for his formula integers 11122mnnmRH Lyman series m 1 n 2 The Balmer series m 2 n 3 Paschen series m 3 n 4 ultraviolet visible infrared 221111nRH 221311nRH 221211nRH integers 11122mnnmRH Bohr provided an explanation for the atomic spectra His model includes both classical and non classical ideas A key figure in the early development of quantum mechanics 1922 Nobel Prize Niels Bohr 1885 1962 1 The electron moves in circular orbits around the proton 2 Only certain electron orbits are stable cannot be explained using classical theory 3 Emission absorption happens when the electron jumps from an initial state to a final state The jump transition cannot be treated classically emission absorption hfEEfi iEfEiEfEhfEEif 4 The circumference of an electron s orbit must contain an integer number of de Broglie wavelengths The standing wave assumption provided by de Broglie h Planck s constant This is also known as quantization Condition electrons can only take certain discrete orbits vmhphee 2vmhnre 2hnvrme nr 2 After some algebra Bohr concluded that the radii of the electron orbits are quantized Only specific orbits are allowed In addition Bohr showed that the energy of a hydrogen atom is also quantized 3 2 1 222 nekmnreenmasselectron constant Coulomb 2eemkh 3 2 1 1 22242 nnekmEeen When n 1 the orbit has the smallest radius called the Bohr radius ao In terms of ao the radii of other orbits can be expressed as 02222 anekmnreen m10529 0102210 ekmraee 3 2 1 m 10529 0 10202 nnanrnmasselectron constant Coulomb 2eemkh The lowest energy state is called ground state The energy of all levels can be expressed as For example n 2 3 2 1 1 1 2 212242 nnEnekmEeeneV6 1322421 ekmEee 3 2 1 eV6 132 nnEn3 4eV26 1322 Emasselectron constant Coulomb 2eemkh All absorption or emission lines of hydrogen can be explained as a result of transitions jumps between Bohr orbits also called energy levels 3 2 1 21 nnEEn 3 2 1 02 nanrnm10529 010220 ekmaee eV6 1322421 ekmEee1 n2 n3 n The discrete spectra lines of hydrogen atom can now be easily understood As the electron makes a jump between different levels it emits or absorb a photon In case of emission finnEEhf 11 222242fieennekmhf 11 422342ifeennekmf 11 4122342ifeenncekm cf Compare to Rydberg formula 11 4122342ifeenncekm 22111nmRH 3424 cekmReeH 17m10097 1 HRmasselectron constant Coulomb 2eemkh A photon is emitted when a hydrogen atom make a transition from n 3 state to n 2 state Calculate the energy wavelength and frequency of the photon You may use either Bohr s or Rydberg s formula J1003 3eV89 14 351 119 3 2 1 eV 1 6 132 nnEnhfEEphoton Hz1057 4106 6261003 31434 19 hEf 21 6 13 31 6 1322 fiEEE1481057 4100 3 fc nm656m1056 67 The ionization energyis the minimum energy needed to completely remove the electron from the atom The uppermost level corresponds to E 0 and n Ionization of hydrogen atom in the ground state Ionization of hydrogen atom in the nth level eV6 13 0 EEIeV6 13 2nEEIn Bohr s result can be generalized to hydrogen like atom An atom is said to be hydrogen like when it contains only one electrons for example He Li Be are all hydrogen like Hydrogen Hydrogen like He Z 2 Li Z 3 Be Z 4 etc 3 2 1 eV 1 6 132 nnEn 3 2 1 eV 6 1322 nnZEn Radii of Bohr orbits in a hydrogen like atom Hydrogen Hydrogen like He Z 2 Li Z 3 Be Z 4 etc m10529 0100 a 3 2 1 02 nZanrn 3 2 1 02 nanrn Calculate the energy of the photon emitted when a He Z 2 jumps from n 3 to n 2 state Solution Frequency and wave length of the emitted photon eV04 6 32 6 13223 E 3 2 1 eV 6 1322 nnZEn23EEEphoton eV6 13 22 6 13222 EeV56 7 6 13 04 6 fchEfphoton Bohr s model of hydrogen atom A model with several ad hoc assumptions It was later replaced by the theory of QUANTUM MECHANICS A quantum system is described by its STATE Associated with each state is a WAVE FUNCTION A quantum state is labeled by a set of QUANTUM NUMBERS There could be many allowed states for a given quantum system e g a hydrogen atom n principle quantum number n 1 2 3 as in Bohr s model Two other quantum numbers also integers emerge from the solution of the quantum mechanical