The magnetic moment vectors `mu_s` and`mu_l` ( associated with the intrinsic spin angular momentum S and orbital angular momentum 1, respectively, of an electron are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by: `mu_s= -(e//m) S`, `mu_l= -(e//2m)l` Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.

If hydrogen atoms (in the ground state ) are passed through an homogeneous magnetic field, the beam is split into two parts. This interaction with the magnetic field shows that the atoms must have magnetic moment. However, the moment cannot be due to the orbital angular momentum since l=0. Hence one must assume existence of intrinsic angular momentum, which as the experiment shows, has only two permitted orientations. Spin of the electron produce angular momentum equal to S=sqrt(s(s+1))(h)/(2pi) where S=+(1)/(2) . Total spin of an atom = +(n)/(2) " or "-(n)/(2) where n is the number of unpaired electrons. The substance which contain species with unpaired electrons in their orbitals behave as paramagnetic substances. The paramagnetism is expressed in terms of magnetic moment. The magnetic moment of an atom mu_(s)sqrt(s(s+1))(eh)/(2pimc)=sqrt((n)/(2)((n)/(2)+1))(eh)/(2pimc)" "s=(n)/(2) impliesmu_(s)=sqrt(n(n+1)) B.M. 1. B.M. (Bohr magneton)= (eh)/(4pimc) If magnetic moment is zero the substance is diamagnetic. If an ion of _(25)Mn has a magnetic moment of 3.873 B.M. Then oxidation state of Mn in ion is :

If hydrogen atoms (in the ground state ) are passed through an homogeneous magnetic field, the beam is split into two parts. This interaction with the magnetic field shows that the atoms must have magnetic moment. However, the moment cannot be due to the orbital angular momentum since l=0. Hence one must assume existence of intrinsic angular momentum, which as the experiment shows, has only two permitted orientations. Spin of the electron produce angular momentum equal to S=sqrt(s(s+1))(h)/(2pi) where S=+(1)/(2) . Total spin of an atom = +(n)/(2) " or "-(n)/(2) where n is the number of unpaired electrons. The substance which contain species with unpaired electrons in their orbitals behave as paramagnetic substances. The paramagnetism is expressed in terms of magnetic moment. The magnetic moment of an atom mu_(s)sqrt(s(s+1))(eh)/(2pimc)=sqrt((n)/(2)((n)/(2)+1))(eh)/(2pimc)" "s=(n)/(2) impliesmu_(s)=sqrt(n(n+1)) B.M. 1. B.M. (Bohr magneton)= (eh)/(4pimc) If magnetic moment is zero the substance is diamagnetic. Which of the following ion has lowest magnetic moment?

The quantum number of four electrons (el to e4) are given below :- {:(,n,,l,,m,,s,,),(e1,3,,0,,0,,+1//2,,),(e2,4,,0,,0,,1//2,,),(e3,3,,2,,2,,-1//2,,),(e4,3,,1,,-1,,1//2,,):} The correct order of decreasing energy of these electrons is :

{:(,"ColumnI",,"ColumnII"),((A),"Orbital angular momentum of an electron",(P),sqrt(s(s+1))(h)/(2pi)),((B),"Angular momentum of an electron in an orbit",(Q),sqrt((n(n+2)))),((C),"Spin angular momentum of an electron",(R),(nh)/(2pi)),((D),"Magnetic moment of atom",(S),sqrt((l(l+1)(h)/(2pi)))):}

Consider the following 3lines in space L_1:r=3hat(i)-hat(j)+hat(k)+lambda(2hat(i)+4hat(j)-hat(k)) L_2: r=hat(i)+hat(j)-3hat(k)+mu(4hat(i)+2hat(j)+4hat(k)) L_3:=3hat(i)+2hat(j)-2hat(k)+t(2hat(i)+hat(j)+2hat(k)) Then, which one of the following part(s) is/ are in the same plane?