Atomic physics - Tran Thi Ngoc Dung

Nội dung text: Atomic physics - Tran Thi Ngoc Dung

1. ATOMIC PHYSICS Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
2. 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.
3. THE SCHRệDINGER EQUATION IN THREE DIMENSIONS 2m  (E U) 0 2 2 E  U  2m Potential KineticEnergy Energy ANS : (ii) must be negative
4. Particle in a Three-Dimensional Box In the box U(x, y,z) 0 (x, y,z,t) (x, y,z)e iEt /  By Variable Separation Technique : (x, y,z) X(x)Y(y)Z(z) Schrodinger equation 2 2(x, y,z) 2(x, y,z) 2(x, y,z) ( ) E(x, y,z) 2m x 2 y2 z2 2 2X 2Y 2Z (YZ XZ XY ) EXYZ 2m x 2 y2 z2 2 2X 2Y 2Z ( ) E 2m Xx 2 Yy2 Zz2 2X 2Y 2Z 2m E 0 Xx 2 Yy2 Zz2 2 2X 2m 3 E 0 2 n n n 2 2 x (x, y,z) sin( x x)sin( Y y)sin( z z) Xx  L L L L 2 2 2 2  X 2m 2 n x n x  2 2 2 2 2 E X 0 X sin( x) E (n z n y n z )  2 2 x x 2 E  L L 2 x 2mL 2mL 2 2 22  Y 2m 2 n Y n y E yY 0 Y sin( y) E y x 2 2 L L 2mL2 2 2 2 2  Z 2m 2 n z n z  EzZ 0 Z sin( z) Ez x 2 2 L L 2mL2
5. Energy – level diagram for a particle in a 3 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
6. HYDROGEN ATOM I. Electron in moving in the electric field caused by the nucleus, and having the potential energy: e2 z U(r) ố 4 or r Schrodinger equation for the electron :  + y 2m x (r) (E U(r))(r) 0  2 2m e2 (r) (E )(r) 0 2  4 or In the spherical coordinate system, and by the variable separation technique, the wave function has the form:  (r) (r,, ) Rn, (r)Y,m(, )
7. Wave function of electron The wave function describing the state of the electron depends on 3 quantum numbers n, ℓ ,m  (r) (r,, ) Rn, (r)Y,m(, ) n = 1, 2, 3, . Principal quantum number ℓ = 0,1, 2 , n-1 Orbital quantum number m = 0, 1, 2,  3, , ℓ Magnetic quantum number Rnℓ(r): Laguerre Yℓm(,): Spherical functions harmonics Zr 1 3 / 2 Z Y0,0 R 2 e a o 4 1,0 a o 3 i 3 i 3 / 2 Zr Y1,1 sine ;Y1, 1 sine 1 Z Zr 8 8 R 2 e 2a o 2,0 a a 3 8 o o Y1,0 cos Zr 8 3 / 2 1 Z Zr 2 2a o 4   R 2,1 e a o 0.53 10 10 m 24 a a o 2 o o mee
8. ENERGY OF ELECTRON IN HYDROGEN ATOM Energy of the electron in the Hydrogen atom is 1 m e4 13.6(eV) E e n 2 2 2 2 n 2(4 o )  n Conclusions 1. Energy of the electron in the Hydrogen atom is quantized and E<0. 2. n increases, the distance between 2 adjacent energy levels decreases. 3. The Ionization energy of hydrogen atom is the energy required to remove the electron from the atom. This is the energy supplied so that the electron can move from E1 to E 13.6eV E E E1 0 ( ) 13.6eV 12
9. n= , E=0 E5=- 0.54eV E4= - 0.85eV E = - 1.54eV 3 The difference between two adjacent energy levels is: E2= - 3.4eV 13.6eV 13.6eV E E E n 1 n 2 2 (n 1) n 2n 1 2 13.6eV 13.6eV 2 2 3 n (n 1) n n , E  E1= -13.6eV
10. 3. For a given n, there are n values of ℓ, for a given value of ℓ , there are 2ℓ +1 values of m 2, For a given n, the number of states that have the enegy En is n  n 1 n(n 1) (2 1) 2(1 2 (n 1)) n 2 n n2  0 2 n 2,E2 3.4(eV) n 2,  0; m 0 2,0,0  1; m 0, 1 2,1,0,2,1,1,2,1, 1, The degeneracy of the energy level E2 is 4. There are 4 states having the same E2.
11. 2 4. Probabilty of finding the electron in a volume dV: | n,,m | dV For the ground state: (n=1, ℓ=0, m=0) : state 1s 3 / 2 r 1 a o 1 1,0,0 R1,0 (r).Y0,0 (, ) 2 e a o 4 probability that the electron is between r and r +dr 2r 1 P(r)dr |  |2 4 r2dr r2e a o dr 1,0,0 3 ao Find the position where the probability of finding the electron is maximum. 2r dP 1 2 2 a o 2r r 2r e 0 dr 3 a a 2 ao o f (r) e o r r 0,r ao
12. SPECTRAL LINES of HYDROGEN ATOM 13.6(eV) En n2 13.6eV 13.6eV  Em En m2 n2 Lyman series : transitions to level n=1 from m=2,3 : Ultraviolet series Balmer series : transitions to level n=2 from m=3, 4, 5 : visible series Paschen: to n=3 from m= 4, 5 : infrared series Bracket: to n=4 from m= 5, 6, infrared series 2 Pfund: to n=5 from m= 6, 7, : infrared series 3
13. n = n = 6 Light of the maximum n = 5 frequency of the Paschen Pfund series = light of minimum n = 4 wavelength of the Paschen series Bracket n=3 max E E3 0 ( 1.5) Paschen 1.24 1.24 min 0.82m max 1.51(eV) n=2 Balmer max, min of Lyman series n=1 Lyman min, max of Lyman series
14. ALKALI METAL ATOMS ố Group 1A ( Li, Na, K ) + ố + Ze+ Ze+ Li (Z=3) Na (Z=11) Alkali Metal The core of the = Valence electron Atom atom , charge +e + ố + Hydrogen ATOM = NUCLEUS, CHARGE + valence +e electron H (Z=1)
15. ENERGY OF VALENce ELECTRON IN ALKALI METAL ATOM Energy levels depend on the 13.6(eV) E quantum numbers n and ℓ n, 2 (n  ) Energy of valence electron can be written as nX Selection rules ℓ 0 1 2 3  1 s p d f ℓ : quantum defect, depends on the orbital quantum nX nS nP nD nF number  and on the atom.  1 Atom s p d f Li 0.412 0.041 0.002 0,000 Na 1.373 0.883 0.010 0.001
16. SPECTRAL LINES of ALKALI METAL ATOMS Li (Z=3), 1s2, 2s1, n=2 , ℓ=0,1 => Energy level 2S, 2P 1. Principal series h 2S nP (n 2,3, ) 2. Sharp series h 2P nS (n 3,4, ) 3. Diffuse series h 2P nD (n 3,4, ) Na(Z=11), 1s2, 2s2 2p6 , 3s1 =>n=3 , ℓ=0,1, 2 => Energy levels 3S, 3P ,3D 1. Principal series h 3S nP (n 3,4, ) 2. Sharp series h 3P nS (n 4,5, ) 3. Diffuse series h 3P nD (n 4,5, ) h 3D nF (n 4,5, ) 4. Fundamental series
17. SPECTRAL LINES of ALKALI METAL ATOMS