Quantum Numbers

Principle Quantum Number  Symbol is n  n = 1, 2, 3,…. In integral positive values  Main energy level occupied by the electron  General distance from the nucleus  More than one electron occupies each energy level  Electrons further from the nucleus have greater energy.  As the orbitals increase in size the electrons spend more time away from the nucleus, and are more loosely held.  Total number of orbitals at each energy level is n 2

Angular Momentum Quantum Number  Symbol – l  Energy sublevel includes all similarly shaped orbitals in a particular sublevel  l = 0 to n-1.  Also referred to by letters where  0 = s  1 = p  2 = d  3 = f

Orbital shapes  s is Spherical  I s orbital at each energy level  p is dumbbell shaped  3 p orbitals at each energy level  d and f are more complex shapes  5 d orbitals at each energy level  7 f orbitals at each energy level  Number of sublevels at each energy level is n

Magnetic Quantum Number  Symbol is m l  Indicates the orientation of each orbital around the nucleus  m l = -l, (-l + 1 ) … 0 … (l + 1), l

s and p orbitals  s is spherical  m l is always 0  P is dumbbell shaped  3 orbitals of p shape  M l = -1, 0, 1

d and f orbitals  d and f orbitals are more complex  d orbitals m l = -2, -1, 0, 1, 2  f orbitals m l = -3, -2, -1, 0, 1, 2, 3

Spin Quantum Number  Symbol m s  2 possible values +1/2 and -1/2  Each orbital can contain at most 2 electrons and they must have opposite spins  Electrons spin on an internal axis