`{:("ColumnI (shell)","ColumnII (value of l)"),((A)2nd,(P)1),((B)3rd,(Q)2),((C)4th,(R)3),((D)1st,(S)0):}`

In Bohr's model, for unielectronic atom, following symbols are used r_(n)z rarr radius of n_(th) orbit with atomic number Z, U_(n,z) rarr Potantial energy of electron , K_(n,z)rarr Kinetic energy of electron , V_(n,z)rarr Volocity of electron , T_(n,z) rarr Time period of revolution {:("ColumnI","ColumnII"),((A)U_(1,2):K_(1,1),(P)1:8),((B)r_(2,1):r_(1,2),(Q)-8:1),((C)V_(1,3):V_(3,1),(R)9:1),((D)T_(1,2):T_(2,2),(S)8:1):}

{:(,"ColumnI",,"ColumnII"),((A),(K.E.)/(P.E.),(P),2),((B),P.E+2K.E.,(Q),-(1)/(2)),((C),(P.E.)/(T.E.),(R),1),((D),(K.E.)/(T.E.),(S),0):}

In case of hydrogen spectrum wave number is given by barv=R_(H)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))] where n_(1)gtn_(2) {:(,"ColumnI",,"ColumnII"),((A),"Lyman series",(P),n_(2)=2),((B),"Balmer series",(Q),n_(2)=3),((C),"Pfund series",(R),n_(2)=6),((D),"Brackett series",(S),n_(2)=5):}

{:(,"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)))):}

{:(,"ColumnI",,"ColumnII"),((A),"The d-orbital which has two angular nodes",(P),3d_(x^(2)-y^(2))),((B),"The d-orbitial with two nodal surfaced from conce",(Q),3d_(s^2)),((C),"The orbital without angular node",(R),4f),((D),"The orbital which has three angular nodes",(S),3s):}

{:(,"ColumnI",,"ColumnII"),((A),"Number of orbitials in then" n^(th)"sheel",(P),2(2l+1)),((B),"Maximum number of electrons in a subshell",(Q),n),((C),"Number of subshell in" n^(th)"sheel",(R),2l+1),((D),"Number of orbitals in a subshell",(S),n^(2)):}

{:(,"ColumnI",,"ColumnII"),((A),"Lyman series",(P),"Visible region"),((B),"Humphery series",(Q),"Ultraviolen region"),((C),"Paschen series",(R),"Infrared region"),((D),"Balmer series",(S),"Far infared region"):}

{:(,"ColumnI",,"ColumnII"),((A),"The radial node of 5s atomic orbital is",(P),1),((B),"The angular node of" 3d_(yz) "atomic orbital is",(Q),4),((C),"The sum of angular node and radial node of" 4d_(xv) "atomic orbital",(R),2),((D),The "angular node of 3patomic orbital is",(S),3):}

A=[{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}] and B=[{:(p_(1),q_(1),r_(1)),(p_(2),q_(2),r_(2)),(p_(3),q_(3),r_(3)):}] Where p_(i), q_(i),r_(i) are the co-factors of the elements l_(i), m_(i), n_(i) for i=1,2,3 . If (l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)) and (l_(3),m_(3),n_(3)) are the direction cosines of three mutually perpendicular lines then (p_(1),q_(1), r_(1)),(p_(2),q_(2),r_(2)) and (p_(3),q_(),r_(3)) are

If P = {:[(0,1,0),(0,2,1),(2,3,0)], Q = [(1,2),(3,0),(4,1)] , find PQ.