Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5574_Библиотеки_им_академика_М_И_Перельмана.pdf
Quantum theory demands a way
of looking at the world of atoms
and molecules very different from the
macroscopic world.
1.1 INTRODUCTION
atom
atoms
atomic orbital.
Chapter Outline (Part A)
1.1 Introduction, 1.2 Wave Mechanical Model of Atom (Atomic Orbital), 1.2.1 Differences Between an Orbit and an Orbital,
1.2.2 Schrodinger Contribution, 1.2.3 Physical Significance of Wave Functions, 1.3 Quantum Numbers, 1.4 Shapes of Orbitals,
1.4.1 Shapes of s Orbitals, 1.4.2 Shapes of p Orbitals, 1.4.3 Shapes of d orbitals, 1.4.4 Signs of Wave Functions, 1.5 Rules for Filling of
Atomic Orbitals (Electronic Configuration of Atoms), 1.5.1 Aufbau Principle, 1.5.2 Pauli's Exclusion Principle, 1.5.3 Hund's Rule of
Maximum Multiplicity, 1.6 Extra Stability of Subshells
STRUCTURE AND
PROPERTIES
1
PART - A
Wave Mechanical Model of Atom
z
x
d
yz
y
x
y
z
d
xz
y
x
z
d
xy
z
y
x
d
xy
2- 2
x
y
z
d
z
2
2
quantum mechanics or wave mechanics
ψ
wave function
1.2 WAVE MECHANICAL MODEL OF ATOM (ATOMIC ORBITALS)
atomic orbitalsa region in space
around the nucleus where there is a maximum probability of nding an electron of a denite energy.
electron cloud
quanta
s, p, d f
s.
Learning Plus
The term stationary does not mean that the
electrons are stationary. The electrons are moving
but their energy is fixed in a particular shell termed
as orbit (fixed energy level).
Figure 1.1 Representation of an orbit and orbital.
(a) An orbital (b) An orbit
3
1.2.1 Differences Between an Orbit and an Orbital (Table 1.1)
Table 1.1 Differences between an orbit and an orbital
S. no. Orbit Orbital
1.
s
p
5.
s
6.
n
where n
1.2.2 Schrodinger’s Contribution
Three-dimensional wave in the electric eld of a positively
charged nucleus probability approach
∂
ψ
+
∂
ψ
+
∂
ψ
+
8pm
+ (E – V)
ψ
= 0
∂x
∂y∂z
h
where xyzm
hEV is the
wave function
∂
2
ψ
∂x
w
x
s
Learning Plus
Alternative Form of Schrodinger-Wave Equation
The Schrodinger wave equation for a system such
as an atom or a molecule can also be written as
Ĥ
ψ
=
E ψ
where Ĥ is the total energy operator called
Hamiltonian operator. The Hamiltonian operator
is the sum of kinetic energy operator (T
ˆ )
and
potential energy operator ( Vˆ), i.e.
Ĥ = T
ˆ + Eˆ
The potential energy operator Vˆ for a system
is normally equal to its expression for potential
energy, V. E is the total energy of the system
and
ψ
(Greek letter psi, pronounced as sigh) is
the amplitude of the wave called wave function.
Substituting the value of Ĥ in the above equation,
we may write:
( T
ˆ + Vˆ
)
ψ
= E
ψ
Therefore, to describe the behaviour of a system,
we write Schrodinger wave equation for the
system in the mathematical forms of Tˆ and Vˆ in
the above equation. Then the equation is solved to
get the values of E and ψ for the system.
4
eigenfunctionorbital.
1.2.3 Physical Significance of Wave Function
wave function
probability density.
NOTEWORTHY POINTS
The wave function of an electron (•
) in the field of nucleus of an atom is called
atomic orbital
.
lt is a three-dimensional amplitude of electron wave.
Particular values of •
ψ
are called eigenfunctions. The values of energies corresponding to these
are called eigenvalues.
The eigenfunction of an electron is called • atomic orbital.
Wave equation is applicable to both atoms and molecules.•
ψ
• may have positive as well as negative values but
2
ψ
(probability) is always positive.
orbital
wave functions orbitals.
atomic orbitals molecular
orbitals
MEMORY FOCUS
Wave Mechanical Model of the Atom
Based on quantum mechanics, Schrodinger gave an equation for an electron in the hydrogen atom. 1.
(Refer to the text for the equation.)
This equation incorporates both the wave nature of the particle and probability nature of measurements. 2.
3.
ψ
indicates the amplitude of the wave function at a given point from the nucleus.
2
4.
ψ
is the probability function and describes the probability of finding an electron within a small space
at a distance from the nucleus.
Space around the nucleus where the probability of finding electrons is maximum (95% or so) is called 5.
orbital.
The probability of finding an electron within a small radial space around the nucleus is called 6. radial
probability distribution.
The plot of 7.
Shapes of orbitals are functional representations of mathematical solutions of Schrodinger equation. 8.
They do not represent any pictures of electric charge or matter.
1.3 QUANTUM NUMBERS
2
ψ
with distance of the electron from the nucleus gives the shapes of various orbitals.
5
1. n)
l )
m)
s)
1. Principal quantum number (n)
n,
Principal quantum number is used to explain the
appearance of main lines in the atomic spectrum
of an element. It determines the main energy
level, the average distance of the electron from
the nucleus and the magnitude of the energy
possessed by the electron.
REMEMBER
n
=
n
=
n =
6
1.
n
n
En = –
pme Z
nh
where m =e =z =h
=
n
=
E
En = –
pme Z
nh
=
–18
n
=
6
6
–1
n
n 6
–1
n 5
–1
n 5
–1
En quantized
nEn
nEn
excited states
2. Azimuthal or angular momentum quantum number (l)
1.
Learning Plus
Quantization means that a quantity cannot vary
continuously to have any arbitrary values but can
change only discontinuously to have some specific
values. Electrons move around the nuclei in fixed
energy levels without undergoing any continuous
loss or gain of energy. It means that the energy of
the electron cannot change continuously but can
have only some definite values. In other words,
energy of an electron is quantized.
hll/(π+)
lnll = 0 to
l = nl
n =ll = 0.
n =ll =l = 1.
n =ll =l =l =
n =ll =l =l =l =
ls, p,
df
Table 1.2 Designation of subshells
Value of 1 Designations of subshell
0
1
s
p
d
f
7
n
=l =s
n =l = 0 (sl = 1 ( p
n
=d
=l = 0 (sl = 1 ( pl
n = l = sl = 1 ( p
l =dl =f
s <p < d< f.
spn.
=
lnp
2p, 3p or 4p
3. Magnetic quantum number (m)
orbitals.
8
1.
m
–l to
+ ll, m
l +
l = 0 (sm m =
s
ss
l
= 1 (pm+p
pPxPyPz.
p
0 11±±
zxy
PPP
m
l =dm++d
d dxydyzd
x
-
y
d
.
d
xydyzdzx
d
xy
d
m
±1 ±1 0
4. Spin quantum number (s)
s
s
s
Learning Plus
The magnetic quantum number is used to explain
the splitting of lines of the atomic spectrum in the
magnetic field (Zeeman effect) or in the electric
field (Stark effect). It determines the orientation
of the subshell and helps in deciding about the
shapes of simple covalent molecules.
9
Figure 1.2 Clockwise and anticlockwise spins of electrons about their own axis.
Table 1.3 Number of orbitals in a subshell and a main shelf
Energy
level
Principal
quantum
number (m)
Possible
values of (l)
Designation
of subshell
Possible
values of (m)
Number of oribitals
In a subshell
(2l + 1)
In a main
shell (n
2
)
0 1s 0 1 1
0 s 0 1
1 p
+-1
p
x
pypz)
0 s 0 1
1 p
+-1
p
x
pypz)
d
++--
5
spdf
++
---
1 ++ 5 +
16
N
––
N
S
S
nlm
s).
Learning Plus
The half integer value of spin quantum number
is in contradiction to integral multiple rule of
quantization of angular moments, but the use of
half integer ½ leads to results that are in complete
agreement with experimental facts.
10
MEMORY FOCUS
Quantum Numbers
The set of numbers used to describe the position and energy of the electron in an atom are called 1.
quantum numbers.
There are four quantum numbers, namely, principal, azimuthal, magnetic and spin quantum numbers.
2.
Quantum numbers are like signatures of electrons. No two electrons can have all the quantum numbers same.3.
Quantum numbers were introduced to explain the spectra of atoms.4.
5. Principal Quantum Number
a. It was proposed by Bohr.
b. Principal quantum number (n) can have values of 1, 2, 3, 4, …. (only integers)
c. It determines the size of the shell as well as energy of the electron.
d. As n increases, the size of the orbit, the distance of the electron from the nucleus and its energy also
increase.
e. It tells us about the main energy level to which the electron belongs.
f. The maximum number of electrons that can be accommodated in a shell is given by 2n2.
g. The maximum number of electrons that can be accommodated in K, L, M and N shells are 2, 8, 18 and
32, respectively.
6. Subsidiary or Azimuthal Quantum Number
a. It was proposed by Sommerfield.
b. It is also known as orbital or angular momentum quantum number and is represented by l.
c. It tells us about the subshell to which the electron belongs in a given main energy level.
d. Its values depend on the value of n.
e. For a given n value, l can have values starting from 0 to (n – 1), i.e. a total of n values.
f. For the values of l equal to 0,1,2,3, the subshell notations are s, p, d and f, respectively.
g. The value of l also indicates the shape of the electron cloud or orbital.
h. The maximum number of electrons that can be accommodated in a given subenergy level is given
by 2 (2l + 1).
Magnetic Quantum Number
7.
a. It was proposed by Lande to explain Zeeman and Stark effects.
b. Magnetic quantum number is denoted by m and its value depends on l.
c. For a given values of l, there can be total of (2l + 1) values of m ranging from – l to + l including zero.
d. Each value of m corresponds to an orbital in a shell with same values of l.
e. Magnetic quantum number describes the orientation of the orbital around the nucleus.
f. For subshell with l = 0, there is only one orientation of the orbital possible.
g. For subshell with l = 1, there can be three orbitals, which can have different orientations.
h. For subshell with l = 2, there can be five orbitals, which can have different orientations.
i. For subshell with l = 3, there can be seven orbitals, which can have different orientations.
j. Number of orbitals in a shell is equal to n2.
8. Spin Quantum Number
a. It was proposed by Uhlenbeck and Goudsmit.
b. Electrons are believed to spin on their own axes in addition to their orbital motion.
c. Spin motion of electron can only be of two types: clockwise and anticlockwise.
d. Spin quantum number is independent of other quantum numbers and can have only two values
+ (clockwise) and – (anticlockwise).
e. For each value of m there will be two possible values of s ( or – ), which means that there can be
only two electrons within an orbital with opposite spin.
f. It is the only quantum number that has nonintegral values.