Quantum Numbers-2 By-N.K.D. Sir Please -Rate review and share this lesson
(iii) Magnetic or Orientation Quantum Number (m): It explains Zeeman effect. It gives the atomic orbital in which the electron is present. It specifies the orientations of atomic orbitals in a magnetic field. The values of 'm' vary from 1, through 0 to +l. Thus, the total values of m are A subshell is made up of atomic orbitals which are described as follows: Sub-shell Values of m (magnetic Atomic orbitals Designations quantum number) m=0 m=-1,0,+ 1 l=0 1=1 PoPoPy ryyUyzZzo@r -y,d, l=3 m=0, 1 , 2, B Complicated
The atomic orbitals Po Py and p are dumb-bell shaped and posses equal energies but differ in their orientations in space. They are called degenerate orbitals. The plane where the electron density is almost zero is called nodal plane 3 Number of nodal plane for np orbital 1 3 3 Pictorial representation of nodal plane: oFor p, atomic orbital xt plane is the nodal plane XZ Plane
Orbital 2px or 3p etc. 2py or 3py etc. 2p or 3p etc. Designation of nodal plane ry 3 The atomic orbitals dxy, dxz, dyz, d j and dz are also degenerate (possess equal energies) 3 The probability of finding the electron in the xy plane in the atomic orbital, d , is not zero. 3 The atomic orbital having dough nut or a belly band or baby soother like shape is dz. It is dumb-bell shaped with a collar of high electron density in the xy plane. Nodal planes for dxy dyz and dx orbitals are 2 each Orbital Nodal plane xz and yz planes xy and yz planes ry and xz planes ry rz 3 f-orbitals are seven in number designated as,
(iv) Spin quantum Number (s): While in motion around the nucleus, the electron spins about its own axis. The spin may be clockwise or anticlockwise. The spinning electron would add to the angular momentum of the electron and therefore changes the energy associated with the electron. Assuming the spin to be quantized, there are two possible values of s, i.e. sd L depending upon whether the electron spins clockwise or anticlockwise. As a convention, the clockwise and anticlockwise spins are represented by an arrow and respectively. Two electrons having the same direction of spin are said to have parallel spins while the two having different direction of spins are said to have anti-parallel spins. For each value of 'm' there are two values of spin quantum number, s and i.e in any atomic orbital only two electrons can be accommodated having anti-paralle t spin. The solution of Schrodinger wave equation gives the principal (n), azimuthal () and magnetic quantum numbers (m) but not the spin quantum number (s). It was introduced on account of the spin of revolving electron.
Significance of Quantum Numbers. The four quantum numbers are of physical significance. They give the address of an electron i.e they are capable of indicating the probable position (shell sub-shell, atomic orbital) and energy of an electron in the atom. For example, if for an electron. n = 3, I = 1, m =-1, and s = +1, then it indicates that the electron is: present in the third shell (M-shell) present in the 3p sub-shell (since for p, 1) -present in the 3p, or 3p, atomic orbital -spinning in clockwise direction. Pauli's Exclusion Principle: This principle states, "No two electrons in an atom can have an identical set of all the four quantum numbers". If three quantum numbers are the same, the fourth will definitely be different. This principle shows that an atomic orbital cannot have more than two electrons and if there are two electrons in any atomic orbital, they will have anti parallel spins. This principle is very helpful in determining the maximum number of electrons in a shell or a sub-shell. For example:
For First Energy Level (K-Shell): n = 1, 1 = 0, (1 s-sub-shell), m = 0 (1 s-atomic orbital) s= opposite spins) These electrons are designated as ls For Second Energy Level (L-Shell): PrincipalAzimuthal Q. Q. number(n) number (I) (Two electrons having Magnetic Q. spin Q. Designation number (m) number(s) m 0 (2s) m =--1 (2p.) m = 0 (2p.) m = 1 (2py I = 0 (29 2s 1 (2p) Total electrons in second shell are eight O Similarly, it can be shown that d-sub-shell (l = 2) can accornmodate 10 and f-subshell can have a maximum of fourteen (14) electrons.
Niranjay Kumar Dwivedi
(N.K.D.Sir) is a Complete Chemistry faculty for IIT~JEE, and NEET examination. with more then 8 year of Teaching experience