2. LEARNING OBJECTIVE
Explain how the Quantum
Mechanical Model of the
atom describes the energies
and positions of the electrons
3. Learning Goals
Compare the Bohr and quantum mechanical
models of the atom.
Explain the impact of de Broglie’s wave
particle duality and the Heisenberg
uncertainty principle on the current view of
electrons in atoms.
Identify the relationships among a hydrogen
atom’s energy levels, sublevels, and atomic
orbitals.
4. Bohr’s Model of the
Atom
Einstein’s theory of light’s dual
nature accounted for several
unexplainable phenomena, but it
did not explain why atomic emission
spectra of elements were
discontinuous.
5. Bohr’s Model of the Atom
In 1913, Niels Bohr, a Danish
physicist working in Rutherford’s
laboratory, proposed a
quantum model for the
hydrogen atom that seemed to
answer this question.
6.
7. Bohr’s Model of the
Atom
The lowest allowable energy state
of an atom is called its ground
state.
When an atom gains energy, it is in
an excited state.
8. Bohr’s Model of the
Atom
Bohr suggested that an electron moves around the
nucleus only in certain allowed circular orbits.
9. Bohr’s Model of the
Atom
Each orbit was given a
number, called the
quantum number.
Bohr orbits are like steps of
a ladder, each at a
specific distance from the
nucleus and each at a
specific energy.
10. Bohr’s Model of the Atom
Hydrogen’s single electron is in the n
= 1 orbit when it is in the ground
state.
When energy is added, the electron
moves to the n = 2 orbit.
11. Bohr’s Model of the Atom
The electron releases energy as it
falls back towards the ground state.
12. Bohr’s Model of the Atom
Bohr’s model explained the hydrogen’s
spectral lines, but failed to explain any
other element’s lines.
For this and other reasons, the Bohr model
was replaced with a more sophisticated
model called the quantum-mechanical or
wave-mechanical model.
13. Quantum Mechanical
Model
Louis de Broglie (1892–1987) hypothesized
that particles, including electrons, could
also have wavelike behaviors.
Electrons do not behave like particles flying
through space.
We cannot, in general, describe their exact
paths.
14. Quantum Mechanical
Model
Heisenberg showed it is impossible to take
any measurement of an object without
disturbing it.
The Heisenberg uncertainty principle states
that it is fundamentally impossible to know
precisely both the velocity and position of a
particle at the same time.
15.
16. Quantum Mechanical
Model
The only quantity that can
be known is the probability
for an electron to occupy
a certain region around
the nucleus.
17. Quantum Mechanical
Model
Schrödinger treated electrons as waves in
a model called the quantum mechanical
model of the atom.
Schrödinger’s equation applied equally well
to elements other than hydrogen (unlike
Bohr’s model).
18. Quantum Mechanical
Model
Orbitals are different from
orbits in that they represent
probability maps that show
a statistical distribution of
where the electron is likely
to be found.
19. Quantum Mechanical
Model
In the quantum-mechanical model,
a number and a letter specify an
orbital.
The lowest-energy orbital is
called the 1s orbital.
It is specified by the number 1
and the letter s.
20. Hydrogen’s Atomic
Orbitals
The number is called the Principal
quantum number (n) and it
indicates the relative size and
energy of atomic orbitals.
n specifies the atom’s major energy
levels, called the principal energy
levels.
28. Hydrogen’s Atomic
Orbitals
Orbitals are sometimes represented by dots, where
the dot density is proportional to the probability of
finding the electron.
The dot density for the 1s orbital is greatest near the
nucleus and decreases farther away from the
nucleus.
The electron is more likely to be found close to the
nucleus than far away from it.
31. Hydrogen’s Atomic
Orbitals
At any given time, hydrogen’s
electron can occupy just one orbital.
When hydrogen is in the ground state,
the electron occupies the 1s orbital.
When the atom gains a quantum of
energy, the electron is excited to one of
the unoccupied orbitals.
32. Quantum Numbers
A set of quantum numbers gives an
information about the atomic orbital
where an electrons may be found
A. principal
B. Azimuthal
C. Magnetic
D. Spin
33. Principal quantum number (n)
a.
- indicates the energy level
n= 1,2,3,4 ….
B. Azimutham Quantum Number (ℓ)
- specifies the sublevel or subshell
ℓ= 0 to n-1
34. c. Magnetic quantum number (mℓ)
- indicates the specific orbital within the sublevel where the
electron is found
-ℓ to +ℓ
Example: n=1, ℓ = 0 , mℓ = 0
n =2, ℓ = 0,1 , mℓ = 0, -1, 0, +1
35. D. Spin quantum Number
- according to Pauli Exclusion
Principle, only a maximum of two
electrons can occupy an orbital,
and they must have opposite
spins to minimize repulsion
between them.
+ ½ or - ½
37. 1.What are the possible sets of
quantum numbers that can
describe a 2p electron in an atom?
2. Give the set of quantum
numbers for each of the six
electrons that occupy the 4p
orbitals
38. 3.Give the electron configuration of
Li. Give the set of quantum
numbers that describe the
outermost electron in lithium as
shown in the orbital diagram below.
4. Give the set of quantum
numbers of Cr
39. Determine the element whose outermost valence
electron is represented by the following quantum
numbers.
a. n=1, l= 0, ml= 0, ms=-1/2
b. n=2, l=1, ml= 0, ms= +1/2
c. n=3, l=1, ml= 0, ms= +1/2
d. n=4, l=2, ml= 0, ms= +1/2
e. n= 6, l=0, ml= 0, ms= -1/2
40. Which of the following are
permissible sets of quantum
numbers?
n = 4, l = 4, ml = 0, ms = ½
n = 3, l = 2, ml = 1, ms = -½
n = 2, l = 0, ml = 0, ms = ³/²
n = 5, l = 3, ml = -3, ms = ½
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