Lecture physics a2 atomic physics

ATOMIC PHYSICS Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 CONTENTS Atomic Physics Particles in 3D Potentials and the Hydrogen Atom Spectral lines of Hydrogen Atom Spectral lines of[.]

ATOMIC PHYSICS Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 CONTENTS Atomic Physics - Particles in 3D Potentials and the Hydrogen Atom - Spectral lines of Hydrogen Atom - Spectral lines of the alkali metal atoms - Angular Momentum, Electron Spin, Atomic States - Pauli Principle Building Atoms and Molecules THE SCHRÖDINGER EQUATION IN THREE DIMENSIONS   E  2m  (E  U)  2    U   m    Potential KineticEnergy Energy ANS : (ii) must be negative Particle in a Three-Dimensional Box In the box U(x, y, z)   ( x , y, z, t )   ( x , y, z)e  iEt /  By Variable Separation Technique :  ( x , y , z )  X ( x ) Y ( y ) Z( z ) Schrodinger equation    ( x , y, z )   ( x , y, z )   ( x , y, z )  (   )  E ( x , y, z) 2 2m x y z 2 2   X  Y  Z  (YZ  XZ  XY )  EXYZ 2m x y z 2 2   X  Y  Z  (   )E 2m Xx Yy Zz  2X  2Y  Z 2m    E0 2 Xx Yy Zz   X 2m  Ex   2 nx nY nz   sin(  ( x , y, z)   x ) sin( y) sin( z) Xx  L L L L nx n 2x      X 2m  E x X   X  sin( x) Ex  (n 2z  n 2y  n 2z )  2 L L E  x  mL 2mL2 n 2y   nY  Y 2m  E y Y   Y  sin( y) Ey  L L x  2mL2 nz n 2z    Z 2m  E z Z   Z  sin( z) Ez  L L x  2mL2 Energy – level diagram for a particle in a dimensional cubic box Having two or more distinct quantum states with the same energy is called degeneracy, and states with the same energy are said to be degenerate HYDROGEN ATOM I Electron in moving in the electric field caused by the nucleus, and having the potential energy: e2 U(r )   z è 4 o r r Schrodinger equation for the electron :  + x  y  2m   ( r )  (E  U(r )) ( r )    2m  e2  ( r )  (E  ) ( r )  4 o r  In the spherical coordinate system, and by the variable separation technique, the wave function has the form:  ( r )  (r, , )  R n, (r)Y,m (, ) Wave function of electron The wave function describing the state of the electron depends on quantum numbers n, ℓ ,m  ( r )  (r, , )  R n, (r)Y,m (, ) n = 1, 2, 3, … ℓ = 0,1, 2…, n-1 m = 0, 1, 2, 3, ,ℓ Principal quantum number Orbital quantum number Magnetic quantum number Rnℓ(r): Laguerre functions R 1,0 R 2, Yℓm(,): Spherical harmonics /  Zr  ao  Z  2   ao   Z     ao  R 2,1  Y0,0  e 3/  Z   24  a o   Zr    e ao   3/  Zr   e  ao   Zr  2a o Zr 2a o Y1,1   Y1,0  4 3 sin ei ; Y1, 1  sin e i 8 8 cos  8 4 o  10 ao   53  10 m mee ...CONTENTS Atomic Physics - Particles in 3D Potentials and the Hydrogen Atom - Spectral lines of Hydrogen Atom - Spectral lines of the alkali metal atoms - Angular Momentum, Electron Spin, Atomic