Question

An electron has a wave function Ynim (r,0,0) = (nr3 e-Kr Yım(0,0). a) What are nlm and their meaning. What additional quantum number added to nlm? b) Plot wave function and radial probability density for Is, 2s, 2p and comment on physical significance. c) Calculate 3s orbital magnetic moment in units of Bohr magnetron, use Bohr model and effective charge given in figure above. Compare it quantum version.

Answer 1

Ywem 18,0,0) = Cn r3 ear Yem 10,0) ma are quantum numbers me oy m a ' nlm n is principle quantum number this describes the energy level or the number of particles (elections) e is azimuthal angular momentum quantum number describes the subshell. is magnetic quantum number describes the orbital of the subshell. mgons → Principle quantum number is integer that is number g electron's shell. The value is 1 or higher never o. The angular momentum quantum qual number is an integer that is the value of the election's orbital (820=p=1) I is greater than or equal to zero and less than = nt. The magnetic quantum number is orientation of the orbital with integer values ranging from al tote. Analogy an γ → w position of shell shape orientation of orbital. of orbit ms ors numbers Another quantum number was added to this cowich describes the spen. According to Pauli. exclusion principle no two election in an atom can have the same set of quantum numbers, spen in half integer value top - down

b Probability density Plots of ware functions. 4 is Rcoop? Physical meaning: when this plots now yanis (Repp? is multiplied by unr it gines. the probability this probability shows the region where the particle is most likely to be found. highest prob. of Mot finding is around peak. 8 - 25 ro 0,4 TROUB? The wroobal 5 10 ry IS 2P | Real? 10 15

2 M = (a me) Jeretio to zme Tereto MB = Boho magneton for 35 l=0 MA rocoto u u =1MB