Complete nomenclature for electron orbitals

Transcription

1 Complete nomenclature for electron orbitals

2 Bohr s model worked but it lacked a satisfactory reason why. De Broglie suggested that all particles have a wave nature. u l=h/p Enter de Broglie again It was the Wave Nature of the electron that determined the nature of the orbits.

3 de Broglie waves One of postulates of Bohr s ugly theory was that angular momentum of the hydrogen atom is quantized: m e vr = nh Why? Not known for 10 years until de Broglie gave a physical interpretation. Electron orbit could be stable only if an integral number of electron wavelengths could be fit inside orbit. 2pr = nl n=1,2,3,

4 de Broglie waves 2pr = nl l=h/m e v (de Broglie wavelength) Plug into top equation u u 2pr=nh/m e v or m e vr=nh/(2p) De Broglie was able to explain the appearance of integers in the Bohr theory as a natural consequence of standing wave patterns 3 wavelengths so n=3

5 Spin magnetic quantum number Another puzzle: close examination of one of the prominent lines in the sodium spectrum shows that it is actually 2 very closely spaced lines No way of understanding this split Uhlenbeck and Goudsmit suggested that there was a 4th quantum number, the spin quantum number, that needed to be introduced Can think of the electron as spinning on its axis u it can either spin up or spin down u no other possibilities u m s =+1/2 (spin up); m s =-1/2 (spin down)

6 Quantum model of atom The previous picture is still a little too classical, though It pictures the electrons as orbiting the nucleus in circular (or elliptical orbitals) But in fact the only reality is y 2, the square of the wavefunction, which gives the probability of the electron to be in a given place at a given time Electron is not confined to any particular orbital distance from the nucleus but has a probability of being at various distances (with a maximum probability at the Bohr radius a o ) Think of the electron as being in an electron cloud y 2 for ground state of hydrogen

7 Electron clouds For hydrogen, the electron cloud looks simple (spherically symmetric) Not so simple for other atoms like carbon u lot of interesting chemistry

8 Picture of atom-1920 s

9 Pauli exclusion principle Each electron in a hydrogen (or any other type of atom) can be specified by the quantum numbers: n,l,m l and m s Wolfgang Pauli (one of founders of quantum mechanics) discovered that no two electrons in the same atom can ever have exactly the same values for the set of quantum numbers u u Pauli exclusion principle helps to explain the electronic structure of complex atoms

10 Filling electron shells As one goes through the periodic table towards higher Z, electrons fill in each subshell starting from the lowest energy level Each subshell has 2(2l+1) electrons in it H (1 electron) is described by either of quantum numbers (1,0,0,1/2) or (1,0,0,-1/2) u 1s 1 He (2 electrons) is described by quantum numbers (1,0,0,1/2) and (1,0,0,-1/2) u 1s 2 Li (3 electrons) has 2 electrons in the 1s subshell and 1 electron in 2s subshell u 1s 2 2s 1

11 Electronic configurations

12 Atomic transitions Consider the possible energy levels of the electrons in an atom. If light is incident on this atom, only photons with an energy equal to the difference DE between two of the energy levels can be absorbed At room temperature, most of the time the atom is in its ground state, so incident photon energies have to correspond to E 2 -E 1, E 3 -E 1, etc Known as stimulated absorption.

13 Spontaneous emission Once an electron is in an excited state, it can fall back to the ground state, emitting a photon.

14 Suppose an atom is in an excited state E 2 and a photon with energy hf=e 2 -E 1 is incident on the atom Incoming photon of this energy increases the probability of the atom returning to the ground state emitting a photon of the same energy hf as the incident photon and in phase with the incident photon These photons can then stimulate other atoms to emit photons The end result can be an intense (many photons), coherent (all photons in phase and of same wavelength) burst of light Stimulated emission

15 Laser (light amplification by stimulated emission of radiation)

16 Bands and band gaps If we have a single atom, then we ve learned about the energy levels possible for electrons in the atom If we have many atoms close together (like in a solid), the energy levels smush out into bands u electrons in the solid can have energies within the bands u and the energies between the bands are forbidden (band gaps) u highest filled band (in ground state) is called valence band u next higher empty band is called conduction band

17 Conductors and insulators Suppose I apply a voltage across a conductor. What happens? Some of the electrons can accelerate and gain energy. This is possible because the conduction band is close in energy to the valence band and there are empty energy states to jump into. This can t happen with insulators where there is too large of an energy gap between.

18 Semi-conductors In between a conductor and an insulator is a semi-conductor where there is a small band gap of about 1 ev u u silicon gallium arsenide The size of the band gap energy E g depends on the temperature of the semiconductor