Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
X-ray fluorescence wikipedia , lookup
Tight binding wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Franck–Condon principle wikipedia , lookup
Hydrogen atom wikipedia , lookup
Molecular Hamiltonian wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
DEPARTMENT OF PHYSICS IIST, Trivandrum Atomic and molecular physics: 2012 EXPLORATIONS –3 1) Sketch the energy level diagram of hydrogen atom, including the fine structure up to n=3. Show the possible transitions. How many different lines are there? ( Z ) 2 n 3 Enj En 1 n2 j 1 4 2 Use: Where, En are the energy eigen values without any corrections. 2) The above equation gives the energy levels with fine structure corrections. a) Show that the correction term does not vanish for any possible combination of n and j, but always reduces the value of uncorrected energy. b) In how many energy levels are the terms of singly ionized Helium with n=3 and n=4 split by the fine structure interaction? c) Sketch the positions of these levels relative to the non-shifted terms and give the amount of shift. Using selection rules indicate which transitions are allowed. 3) (a) For a given Z and n ≠ 1, derive the energy difference between two extreme components of a fine structure multiplate. (b) For a given Z, n ≠ 1 and l ≠ 1derive the energy separation between two levels corresponding respectively to j1=l+1/2 and j2=l-1/2. 4) aShow that the Hamiltonian of a free electron in a uniform time independent magnetic field pointing along z axis is given by, H = Hxy + Hz With, H xy 1 1 p x2 p y2 m L2 x 2 y 2 2m 2 And 1 2 p z L ( LZ 2 S z ) 2m Where, L B / 2 L is the Larmor frequency. Hz b) Using the fact that H can be written as a square, H = (p+eA)2/(2m),and that the Hxy of the harmonic motion in XY plane is invariant under reflection, show the energy eigen values are given by, 2k 2 L (2r 2ms 1) 2m Where, k , r = 0, 1, 2, 3,…… and ms 1 2 For a given k and ms the discrete energy levels E labeled by quantum number rare the Landau levels. c) In neutron stars the magnetic fields of the order of 108 T may occur. Find the energy separation between the adjacent Landau levels. What is the size of the region to which the motion in the XY plane is confined? Bottom line: Who are these people? Is the idea right? “……” said …….. “Winter is approaching, I am worried about my plants which I brought from India, and they need sunlight” “Easy” said …….. “Keep them in artificial light” “Which colour?” asked ……… “Green light of course, its elementary my dear…….” Hint: This is a very famous pair of a D….. and a D…….. (by profession).