CHM 1210 1st Edition Lecture 8Outline of last LectureI. Atomic Structure: explaining the properties of elementsa. Wave theoryb. Atomic spectrac. Quantum theoryOutline of current lecture II. Atomic structure: explaining the properties of elementsd.electrons and wavese. quantum numbersCurrent Lecture:The DUAL nature of electrons – French graduate student, Louis de Broglie (1892-1987) Obs: § If electromagnetic radiation behaves as a particle, could a particle in motion, such as an electron, behave as a wave? _yes_, any moving particles has _wave like properties_. • de Broglie wavelength (λ): § __λ= h/(mc) or λ= h/(mh)__________ m = mass of electron (in kg) v = velocity (in m/s) h = Plank’s constant = 6.626 x 10-34 J s Definitions: Linear waves Standing wave = a wave confined to a given space with a wavelength, λ, related to the length L of the space by _L=n (λ/2)__, where n is a whole number. • Obs: • Wavelength: ___λ=21___ • • Harmonic frequencies: ___________ n = 1 : ____the fundamental structures_________ n = 2 : __first harmonic n = 3 : _second harmonic________ Obs: • Electrons behave like _circular waves_oscillating around nucleus. • These circular waves have _no defined stationary ends, and account for _the stability_of the energy levels in Bohr’s model. - German physicist Werner Heisenberg (1901-1976) These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Heisenberg Uncertainty Principle: One cannot simultaneously know __the exact position and ___exact momentum __of an electron. ∆x∆m∆vz(h/4pi)∆� = �ℎ���������������ℎ������������ℎ���������m = �ℎ��������ℎ���������∆� = �ℎ���������������ℎ������������ℎ���������ℎ = �ℎ�������′���������In 1925, the Austrian physicist, Erwin Schrödinger (1887-1961) • Proposed the quantum mechanical model of the atom, which focuses on the _wave like properties__of the electron. • Developed mathematical equations to describe behavior of _electron waves__, which became the basis of quantum mechanics. Schrödinger solve Wave function Probability of finding Waveelectron in a region equation or orbital (Y) of space (Y 2) Obs: A wave function is characterized by three parameters called quantum numbers, n, l, ml. 1) Principal Quantum Number (n) • Describes __the size and energy level_ of the orbital o Commonly called __shells_________ • Positive integer: n=1,2,3,4,5,…__________ • As the value of n increases: • The size of orbitals ____increases__ and the energy of the e- in these orbitals increases____. • The average distance of the e- from the nucleus ____increases___. 2) Angular-Momentum Quantum Number (l) • Defines _3-d shape_____of the orbital • Commonly called _subshells__ • There are n different shapes for orbitals:_l= 0,…., n-1_ • If n = 1 then l = _0__ • If n = 2 then l = _0,1• If n = 3 then l = _0,1,2_ and so on • Commonly referred to by letter 3) Magnetic Quantum Number (ml )• Defines __spatial orientation of the orbital • There are 2l + 1 values of ml and they can have any integral value from ml= -1,…,0….1• If l = 0 then ml = 0_(s) If l = 1 • If l = 1 then ml = _-1,0,1_(p) • If l = 2 then ml = _-2,-1,0,1,2 (d)_ and so on Obs: • There are _n__ subshells in the nth shell.• There are __n^2 orbitals in the nth shell. • There are __2l+1_orbitals in each subshell. Practice problem: a) What are the names of all the subshells in the n = 4 shell? Names: s, p,d,fb) How many orbitals are in all of the subshells of the n = 4 shell? 163.6 Quantum numbers Electron Spin – two students at the University of Leiden in the Netherlands, Samuel Goudsmit (1902-1978) and George Uhlenbeck (1900-1988) Obs: • Not all spectra features are explained by wave equations. The appearance of “doublets” (a pair of lines) in atoms with a single electron in outermost shell are due to the ___electron spin____. • Electrons have spin which gives rise to a tiny magnetic field and to a _spin quantum number__. Otto Stern (1888-1969) and WaltherGerlach (1889-1958) Obs: Spinning of electron creates a magnetic field oriented either __up and