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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5574_Библиотеки_им_академика_М_И_Перельмана.pdf
Nodes
3s
1s
2s
Node
1.4 SHAPES OF ORBITALS
Based on probability distribution: s
s
s
Based on quantum number:
1.4.1 Shapes of s Orbitals
sl =l =m =
s
s
xyz
n).
ns
s
11
Difference between 1s and 2s Orbitals
ss
node
Figure 1.3 The electron density distribution in the 1s, 2s and 3s atomic orbitals. The overall size of the
orbital increases with increasing n. The number of nodal spheres for an ns orbital is (n – 1).
12
2p Orbitals
2px Orbital
x
y
x
y
z
2py Orbital 2pz Orbital
ss
s
s
s
n n
1.4.2 Shapes of p Orbitals
Based on probability distribution:
pp
a dumb-bell
p
nodal plane.
Based on quantum number: pl
=l =m
+
1. there are three ppxpypz
Figure 1.4 Shapes of p orbitals.
pxpypzx, y
z
p
pxxpy
ypzzp
++
x
z
y
p
x
yz Nodal
plane
+
x
y
z
xz Nodal
plane
p
y
z
x
y
+
xy Nodal
plane
p
z
p
ps
n.)
p
Figure 1.5 Nodal plane in p orbitals.
13
the p
pn ppp has two.
p
nodal plane.
1.4.3 Shapes of d Orbitals
Based on quantum number: dl =m++
ddxydxzd
x
d
.
z
d
1. d
the dxy dyz d
xy yz xz
clover leaf shape.
d
xy
x
xz
dxy
zxy
xy
It should be noted that a nodal plane is a plane of
zero electron density separating the lobes of a p
or d orbital. On the other hand, a node is a region
of zero electron probability between the regions
of high electron probability within an orbital.
REMEMBER
14
z
z
z
z
x
x
x
x
x
y
y
y
y
y
d
yz
d
xz
d
xy
d
x
2
– y
2
d
z
2
z
the d
z
dumb-bell
Figure 1.6 Shapes of d orbitals.
5. d d d
d
x
in the other set there are three dd
d
dyz
xy
xz
2
z
d
Based on probability distribution: d
dn
-dd
= n - l - 1.
1.4.4 Signs of Wave Functions
is
s
Orbitals
s
p
Orbitals
p
p
pz
z
y
y
y
z
+
−
−+
+
−
z
z
xx
x
2p
y
2p
x
2p
z
15
cos
cos
θ
θ
θ
θ
0 15 60
1.0 0.866 0.5 0
105 150 165 180
–0.5 –0.866 –1.0
Figure 1.7 Sign pattern of p orbitals.
pypxpz
the p
d
Orbitals
d+
the d
1. s
p
d
MEMORY FOCUS
Shapes of Orbitals
1. The shape of the orbital is determined by azimuthal quantum number l.
2. If l = 0, the orbital notation is s, similarly if l = 1, 2, 3 and 4, the orbitals are given by the symbols p, d, f and
g, respectively.
3. s Orbital is spherical in shape, p orbital is dumb-bell shaped, d orbital is double dumb-bell shaped and f
orbital has complicated shapes.
4. s Orbital has only one lobe; each p orbital has 2 lobes; each d orbital has 4 lobes; each f orbital has 8
lobes.
16
5. In a given p sublevel, there are three p orbitals perpendicular to each other; they are designated as
p
, py and pz, respectively (for m values –1, 0 and +1).
x
6. In a given d sublevel there are five d orbitals. They are designated as d
, dyz, dzx, d
xy
x2–y
and d
2
respectively.
7. The d
8. The d
9. The d
, dyz and d
xy
has the lobes along the x and y axes.
2
x2–y
orbital has only two lobes along the z axis and a ring in the x - y plane.
2
z
orbitals have lobes in between their respective axes at 45° with respect to axes.
zx
10. As the value of principal quantum number (n) increases, the size of the orbital increases.
11. s Orbital has no direction property, whereas all other orbitals have special orientations.
12. An electron in the p orbital can be found in either of the lobes with equal probability.
NOTEWORTHY POINTS
1. Degenerate orbitals
Atomic orbitals with same energy are known as degenerate orbitals. Thus there are (2l + 1) degenerate
orbitals for each value of l. Hence each value of 1 will have 2 × (2l + 1) electrons.
2. Nodes and nodal planes
a. The region where the probability of finding an electrons is zero is called nodal region or simply a
node.
b. The plane in which the probability of finding an electron is zero is called a nodal plane.
c. s Orbital has no nodal planes, p orbital has one, d orbital has two and f orbital has three nodal
planes.
d. For d
e. For d
f. d
g. d
orbital, YZ plane is the nodal plane, for py orbital ZX plane is the nodal plane; for pz orbital, XY
xy
plane is the nodal plane.
orbital, YZ and ZX planes are nodal planes. Similarly for dyz and dzx orbitals XY and XZ planes
xy
and YZ and XY planes are nodal planes.
2
2
-
orbital has two nodal planes. They are two planes at 90° to each other, which make 45° to X
x
y
and Y axes.
2
2
, dyz and dxz orbitals are called dε or t
xy
orbitals, whereas d
2g
x
–
2
, d
are called dz or eg orbitals.
y
z
,
2
z
1.5 RULES FOR FILLING OF ORBITALS OR ELECTRONIC CONFIGURATION OF ATOMS
electronic conguration of atoms
1.5.1 Aufbau Principle
Aufbauprinzip
1s
2s 2p
3s 3p
4s
5s
6s
7s 7p
4p 4d 4f
3d
5p 5d 5f
6p 6d
is 1sspspspsdpsfdps
psd
nl
n
+ l
n
+ l rule or Bohr Bury’s rule
nl (n
n + l
+ l) rule.
Figure 1.8 Sequence of filling
atomic orbitals.
sn + l =+ 0 =p (n + l =+ 1 =
sddn
+ 0 =sds
+ l =+=sn + l=
17
n + l n has lower
pn
+ l =+ 1 =sn + l =+ 0 =n + lp
ns
1.5.2 Pauli’s Exclusion Principle
n, l, m
s
exclusion principle.
Applications
1. An orbital cannot have more than two electrons:
n, lm
s s
18
an orbital can accommodate at the
maximum two electrons having opposite spins.
Electron capacity of subshells and shells:
a. K shell: n = 1; ll =m
i.e. m
=s
n
= 1 l = 0 m = 0 s
= 1 l = 0 m = 0 s
n
l
L shell: n =l l = 0 (sl = 1 (pl =
m m =l =m m = -+1.
sm
= 0 (s
n l = 0 m = 0 s
n l = 0 m = 0 s
n l = 1 m = –1 s
n l = 1 m = –1 s
n l = 1 m = 0 s
n l = 1 m = 0 s in p
n l = 1 m = +1 s
n l = 1 m = +1 s
l = 0 (sl = 1 (ps
n =sl =
pl =dl =
in s
6
6
19
n l m s
0 0
1 +1 8
0
–1
+1
0
–1
Designation and
number of orbitals
s (one)
p (three)
d
Electrons
present
6
10 18
Total number of
electrons
1.5.3 Hund’s Rule of Maximum Multiplicity
Electron lling will not take place in the orbitals of same energy until all the available orbitals of the
given subshell contain one electron each with parallel spin.
p, df
20
ssp. As p
p
ssp
p
Z =
d
Explanation