The document outlines the quantum mechanical model of the atom, detailing the concept of quanta and the contributions of physicists like Max Planck, Albert Einstein, and Niels Bohr to our understanding of atomic structure. It explains how electrons occupy quantized energy levels and introduces quantum numbers to describe their positions and behaviors within an atom. Additionally, it highlights significant contributions from key figures in quantum mechanics, including the development of foundational theories such as wave mechanics and the uncertainty principle.

1. The Quantum Mechanical
Model of the Atom

2. 
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.

3. 
 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.
Why Is Energy Quantized

4. 
The Dual Nature of Light as stated
by Louis de Broglie

5. 
 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

6. 
 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.
The Bohr Model of the Atom (cont’d)

7. 
 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.
Orbitals and Quantum Numbers

8. 
When we say “orbital,” the image below
is what we picture in our minds.

9. 
 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.
Quantum Numbers?

10. 
 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.
Principal quantum number (n)

11. 
 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
Azimuthal quantum number (l)

12. 
 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.
Spin quantum number (ms)

13. 
 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.
Magnetic quantum number (ml)

14. 
 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.
What You Should Keep In Mind About
Quantum Numbers and Electron Shells

15. 
Value of l (subshell) Letter Designation
0 s
1 p
2 d
3 f
4 g
s, p, d, f, and g?

16. 
 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.
What do we mean by “1s, 2s, 3d,
5f…”?

17. 
The following figure shows the
shapes of the s, p, and d orbitals.

18. 
 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.
What in the world does it mean?

19. They are the so-called “Quantum Mechanics
Masters”. Following below are the reasons
why we should thank them.

20. 
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.

21. 
 Max Planck- He is a German theoretical
physicist who originated quantum theory, which
won him the Nobel Prize in Physics in 1918.
 Albert Einstein- He is best known in popular culture
for his mass–energy equivalence
formula E = mc2 (which has been dubbed "the
world's most famous equation").
 Niels Bohr- He is a Danish physicist who made
foundational contributions to understanding atomic
structure and quantum theory, for which he received
the Nobel Prize in Physics in 1922.
What did they do?

22. 
 Louis de Broglie- He is a French physicist who made
groundbreaking contributions to quantum theory. In his 1924
PhD thesis he postulated the wave nature of electrons and
suggested that all matter has wave properties.
 Max Born- He was a German physicist and mathematician who
was instrumental in the development of quantum mechanics.
He also made contributions to solid-state
physics and optics and supervised the work of a number of
notable physicists in the 1920s and 30s. Born won the
1954 Nobel Prize in Physics for his "fundamental research in
Quantum Mechanics, especially in the statistical interpretation
of the wave function“.
What did they do?

23. 
 Paul Dirac- He was an English theoretical physicist who made
fundamental contributions to the early development of
both quantum mechanics and quantum electrodynamics. He
was the Lucasian Professor of Mathematics at the University of
Cambridge, a member of the Center for Theoretical Studies,
University of Miami, and spent the last decade of his life
at Florida State University.
 Among other discoveries, he formulated the Dirac equation,
which describes the behavior of fermions and predicted the
existence of antimatter. Dirac shared the Nobel Prize in
Physics for 1933 with Erwin Schrödinger, "for the discovery of
new productive forms of atomic theory". He also did work that
forms the basis of modern attempts to reconcile general
relativity with quantum mechanics.
What did they do?

24. 
 Werner Heisenberg- He formulated the 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.
 Wolfgang Pauli- He formulated the Pauli exclusion
principle, perhaps his most important work, which
stated that no two electrons could exist in the same
quantum state, identified by four quantum numbers
including his new two-valued degree of freedom.
What did they do?

25. 
 Erwin Schrödinger- He was a Nobel Prize-
winning Austrian physicist who developed a
number of fundamental results in the field
of quantum theory, which formed the basis of wave
mechanics: he formulated the wave equation
(stationary and time-dependent Schrödinger
equation) and revealed the identity of his
development of the formalism and matrix
mechanics. Schrödinger proposed an original
interpretation of the physical meaning of the wave
function.
What did they do?

26. 
 Richard Feynman- He was an American theoretical
physicist known for his work in the path integral
formulation of quantum mechanics, the theory
of quantum electrodynamics, and the physics of the
superfluidity of supercooled liquid helium, as well
as in particle physics (he proposed
the parton model).
What did they do?

27. 
D’Picture of the Day