If an electron in an atom has an orbital angular momentum with ml = 5, what are the components (a) Lorb,z and (b) orb,z? If the atom is in an external magnetic field that has magnitude 33 mT and is directed along the z axis, what are (c)the potential energy Uorb associated with the electron\'s orbital magnetic dipole moment and (d) the magnitude of the potential energy Uspin associated with the electron\'s spin magnetic dipole moment? If, instead, the electron has ml = -5, what are (e) Lorb,z, (f) orb,z, (g) the potential energy Uorb associated with the electron\'s orbital magnetic dipole moment and (h) the magnitude of the potential energy Uspin associated with the electron\'s spin magnetic dipole moment?
If an electron in an atom has an orbital angular momentum with ml = 5, what are the components (a) Lorb,z and (b) orb,z? If the atom is in an external magnetic field that has magnitude 33 mT and is directed along the z axis, what are (c)the potential energy Uorb associated with the electron\'s orbital magnetic dipole moment and (d) the magnitude of the potential energy Uspin associated with the electron\'s spin magnetic dipole moment? If, instead, the electron has ml = -5, what are (e) Lorb,z, (f) orb,z, (g) the potential energy Uorb associated with the electron\'s orbital magnetic dipole moment and (h) the magnitude of the potential energy Uspin associated with the electron\'s spin magnetic dipole moment?
(a) Lorb,z =ml*h= 5*(6.6*10-34)=3.3*10-33
(b) orb,z= -ml*B
B= eh/4m =-9.274*10-24 J/T (bhor magneton)
therefore, orb,z=-5*(-9.274*10-24)
=4.637*10-23
(c) Potential energy Uorb = -orb,z . Bext
= -4.637*10-23 * (33*10-3)
=-1.53*10-24
(d)spin magnetic dipole moment component in z direction = s,z=eh/4m=9.274*10-24 J/T
potential energy Uspin = -s,z . Bext= -9.274*10-24 *(33*10-3)
=-3.06*10-25
(e)Lorb,z =ml*h= -5*(6.6*10-34)= -3.3*10-33
(f) orb,z= -ml*B
B= eh/4m =-9.274*10-24 J/T (bhor magneton)
therefore, orb,z=-(-5)*(-9.274*10-24)
= -4.637*10-23
(g) Potential energy Uorb =-orb,z . Bext
= -(-4.637*10-23) * (33*10-3)
=1.53*10-24
(h)spin magnetic dipole moment component in z direction = s,z=eh/4m=-9.274*10-24 J/T
potential energy Uspin = -s,z . Bext= 9.274*10-24 *(33*10-3)
=3.06*10-25
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