Question #195586

For an electron in the l = 2 state:

(a) enumerate all the possible values of quantum numbers j and mj ;

(b) draw the corresponding vector diagrams;

(c) estimate the maximum value of the spin-orbit coupling energy E. 


1
Expert's answer
2021-05-20T10:09:31-0400

l=2n=3l=2\\\therefore n=3

(a) s=1/2s=1/2

j=(n+s),(ns)j=(n+s),(n-s)

j=(5/2),(3/2)j=(5/2),(3/2)


For j = 5/2

jm=j(j+1)2jm=j(j+1)\hbar^2

jm=3542jm=\dfrac{35}{4}\hbar^2


For j = 3/2

jm=1542jm=\dfrac{15}{4}\hbar^2


(c) ΔEso=αZ34m2c1r3[j(j+1)l(l+1)s(s+1)]\Delta E_{so}=\alpha\dfrac{Z\hbar^3}{4m^2c}\dfrac{1}{r^3}[j(j+1)-l(l+1)-s(s+1)]

s=1/2, l=2, j=5/2s=1/2,\space l=2,\space j=5/2

ΔEso=αZ34m2c1r3[52(52+1)2(2+1)12(12+1)]\Delta E_{so}=\alpha\dfrac{Z\hbar^3}{4m^2c}\dfrac{1}{r^3}\bigg[\dfrac{5}{2}\bigg(\dfrac{5}{2}+1\bigg)-2(2+1)-\dfrac{1}{2}\bigg(\dfrac{1}{2}+1\bigg)\bigg]

ΔEso=2αZ34m2c1r3\Delta E_{so}=2\alpha\dfrac{Z\hbar^3}{4m^2c}\dfrac{1}{r^3}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS