Download quantum number - WordPress.com

The Quantum Mechanical
Model of the Atom
What does “quanta” mean?

 In physics, a quantum (plural: quanta) is the
minimum amount of any physical entity involved in
an interaction. Behind this, one finds the
fundamental notion that a physical property may be
"quantized," referred to as "the hypothesis
of quantization". This means that the magnitude can
take on only certain discrete values.
Why Is Energy Quantized

 After Max Planck determined that energy is released
and absorbed by atoms in certain fixed amounts
known as quanta, Albert Einstein took his work a
step further, determining that radiant energy is also
quantized—he called the discrete energy
packets photons. Einstein’s theory was that
electromagnetic radiation (light, for example) has
characteristics of both a wave and a stream of
particles.
The Dual Nature of Light as stated
by Louis de Broglie

The Bohr Model of the Atom

 In 1913, Niels Bohr used what had recently been
discovered about energy to propose his planetary
model of the atom. In the Bohr model, the neutrons
and protons are contained in a small, dense nucleus,
which the electrons orbit in defined spherical orbits.
He referred to these orbits as “shells” or “energy
levels” and designated each by an integer: 1, 2, 3, etc.
The Bohr Model of the Atom (cont’d)

 An electron occupying the first energy level was
thought to be closer to the nucleus and have lower
energy than one that was in a numerically higher
energy level. Bohr theorized that energy in the form
of photons must be absorbed in order for an electron
to move from a lower energy level to a higher one,
and is emitted when an electron travels from a
higher energy level to a lower one. In the Bohr
model, the lowest energy state available for an
electron is the ground state, and all higher-energy
states are excited states.
Orbitals and Quantum Numbers

 In the 1920s, Werner Heisenberg put forth
his uncertainty principle, which states that, at any
one time, it is impossible to calculate both the
momentum and the location of an electron in an
atom; it is only possible to calculate
the probability of finding an electron within a given
space. This meant that electrons, instead of traveling
in defined orbits or hard, spherical “shells,” as Bohr
proposed, travel in diffuse clouds around the
nucleus.
When we say “orbital,” the image below
is what we picture in our minds.

Quantum Numbers?

 To describe the location of electrons, we use quantum
numbers. Quantum numbers are basically used to
describe certain aspects of the locations of electrons. For
example, the quantum numbers n, l, and ml describe the
position of the electron with respect to the nucleus, the
shape of the orbital, and its special orientation, while the
quantum number ms describes the direction of the
electron’s spin within a given orbital.
 Below are the four quantum numbers, showing how they
are depicted and what aspects of electrons they describe.
Principal quantum number (n)

 It has positive values of 1, 2, 3, etc. As n increases, the
orbital becomes larger—this means that the electron
has a higher energy level and is less tightly bound to
the nucleus.
Azimuthal quantum number (l)

 It has values from 0 to n – 1. This defines the shape of
the orbital, and the value of l is designated by the
letters s, p, d, and f, which correspond to values
for l of 0, 1, 2, and 3. In other words, if the value
of l is 0, it is expressed as s; if l = 1 = p, l = 2 = d,
and l = 3 = f
Spin quantum number (ms)

 It specifies the value for the spin and is either +1/2
or -1/2. No more than two electrons can occupy any
one orbital. In order for two electrons to occupy the
same orbital, they must have opposite spins.
Magnetic quantum number (ml)

 It determines the orientation of the orbital in space
relative to the other orbitals in the atom. This
quantum number has values from -l through 0 to +l.
What You Should Keep In Mind About
Quantum Numbers and Electron Shells

 Orbitals that have the same principal quantum number, n,
are part of the same electron shell. For example, orbitals
that have n = 2 are said to be in the second shell. When
orbitals have the same n and l, they are in the
same subshell; so orbitals that have n = 2 and l = 3 are
said to be 2f orbitals, in the 2f subshell.
 Finally, you should keep in mind that according to
the Pauli exclusion principle, no two electrons in an atom
can have the same set of four quantum numbers. This means
no atomic orbital can contain more than two electrons, and
if the orbital does contain two electrons, they must be of
opposite spin.
s, p, d, f, and g?

Value of l (subshell)
Letter Designation
0
s
1
p
2
d
3
f
4
g
What do we mean by “1s, 2s, 3d,
5f…”?

 When chemists describe one particular subshell in an
atom, they can use both the n value and the subshell
letter — 2p, 3d, and so on. Normally, a subshell
value of 4 is the largest needed to describe a
particular subshell. If chemists ever need a larger
value, they can create subshell numbers and letters.
The following figure shows the
shapes of the s, p, and d orbitals.

What does it mean?

 As shown in the top row of the figure (a), there are
two s orbitals — one for energy level 1 (1s) and the
other for energy level 2 (2s). The s orbitals are
spherical with the nucleus at the center. Notice that
the 2s orbital is larger in diameter than the 1s orbital.
In large atoms, the 1s orbital is nestled inside the 2s,
just like the 2p is nestled inside the 3p.
 The second row of the figure (b) shows the shapes of
the p orbitals, and the last two rows (c) show the
shapes of the d orbitals. Notice that the shapes get
progressively more complex.
Left to right: Max Planck, Albert Einstein, Niels
Bohr, Louis de Broglie, Max Born, Paul Dirac, Werner
Heisenberg, Wolfgang Pauli, Erwin Schrödinger, and
Richard Feynman.

Energy levels and multielectron atoms

 To construct a model of an atom, follow these two
rules:
(1) Aufbau Principle – Electrons always enter orbitals
of the lowest energy first.
(2) There is a maximum number of electrons for each
energy level. The number is given by 2n2 where n is
the principle quantum number.
Pauli Exclusion
Principle

 An atomic orbital may describe at most two
electrons. To occupy the same orbitals, two electrons
must have opposite spins. Spin is a quantum
property of electrons and may be clockwise
(represented by an upward pointing arrow ↑) or
counterclockwise (represented by a downward
pointing arrow ↓).
Hund’s Rule

 When electrons occupy orbitals of equal energy, one
electron enters each orbital until all the orbitals
contain one electron with spins parallel (either all the
spins are clockwise or all the spins are
counterclockwise). Second electrons then add to
each orbital so that their spins are paired with the
first electrons in the orbital.
Steps to Writing the
Electron Configuration of
an Atom

 Step 1
 Get a Periodic Table of Elements
 Find out how many electrons the atom has. On the
periodic table, the atomic number is the number of
protons of the atom, and thus equals the number of
electrons in an atom with zero charge.
Step 2: Mnemonic for
Filling Orbitals

Step 3

• Put one electron into the highest energy orbital
available, starting with 1s (holds a maximum of two
electrons). Fill the orbitals in this order (the number in
superscript following the sublevel is the maximum
number of electrons it can hold):
– 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2
5f14 6d10
– Note: Energy level changes as you go up. For example,
when you are about to go up to the 4th energy level, it
becomes 4s first, then 3d. After the fourth energy level,
you'll move onto the 5th where it follows the order once
again. This only happens after the 3rd energy level!
Step 4

• Once you've put every electron into an orbital
(according to the order), write the configuration as
shown at the end of step 3. Only write the orbitals
that contain electrons.
• So, an uncharged antimony atom's electron
configuration would be 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6
5s2 4d10 5p3. Notice that the superscript number
following 5p is 3. That's because only three electrons
are in the 5p sublevel, so the sublevel is not
completely occupied (it lacks three more electrons).