Question

-content-disposition-inline%3B%; -+ QEFit to page Page (a) Using diagrams to support your answer, provide a description of the Stern-Gerlach experiment and how this led to the concept of intrinsic angular momentum. [5 marks (b) Use Hund's rules to find the ground state quantum numbers L and S for nitrogen which has electronic configuration 1s22s22p3 [4 marks] (c) It can be shown that the z-component of orbital angular momentum commutes with both the square of position (in spherical coordinates) and momentum i.e.: IL, and o (i) Explain the physical meaning of these equations. [2 marks) (ii) Use these relations to explain why the Hamiltonian commutes with all three components of L [3 marks] (d) The radial wave function for the n = 1,1 = 0 state of hydrogen is given by: R(r) =-3/2 e-r/ao do Show that the radial probability density has its maximum value at r ao. [6 marks] TOTAL: 20 marks]

Answer 1

a-atom from am oen basses th rough he mon- Cmd gives -fhe intensity atth. tuo pla ess on -thu Ccreen which shout the unpaived eleetan - atom have tuso sbin Scvean oven Intent 方 2 汀= L+8_ 3.to々.3. 2. Ground stateす2SH 4

t shows thst thy g are comute to each other ie the position vector ts conserved quan anJular msmentun)as cse as p. This also means than con be ure be mects une simultaneous toni an İs olso comsened cotth that, it mean s enead is comsrved durin tRe motion Both are y mengurabe at the same time recis 4- for maximem yadial prbbily dansity 4- 2Y Do