5.
1 – Discrete Energy Levels
(Describe the photon model. )
•Photons are fundamental particles that make up all forms of
electromagnetic radiation.
•A photon is a massless ‘packet’ or ‘quantum’ of electromagnetic
energy.
•This means that the energy is not transferred continuously but as
discrete packets of energy.
•Each photon carries a specific amount of energy, and transfers this
energy all in one go. I s
n 3
n
Fi
PHY71 n t ev
5.1 – Discrete Energy Levels
The energy of a photon directly related to the
frequency and inversely to the wavelength.
•The energy of a photon is related to its frequency
by the equation: ! = h"
•The energy of a photon is inversely related to its
wavelength by the equation: !"
E=O E hf
J #
g
• Energy is converted from joules to #$:
1.6 x 10-19 % = 1 #$
f f 1034
PHY71
charge Electron h 6.63
C 3 108m s
The Bohr Model
1. Electrons move in circular orbits
2. Only certain electron orbits are
stable and allowed
3. Radiation is emitted when the
electron jumps from a higher to
lower energy state:
Ei - E f = hf Ei > E f
The frequency of the radiation is
independent of the frequency of
the electron’s orbital motion.
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The atomic energy levels.
•The electrons in an atom can have only
certain specific energies (or quantized).
•These energies are called electron
energy levels.
•They can be represented as a series of
statcked horizontal lines increasing in
energy. II
PHY71 h
The Bohr Model
4. Circumference of orbit must
contain an integral number of de
Broglie wavelengths:
2p r = nl n = 1, 2, 3,...
!"
E=
#
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Energy Levels
Electrons can occupy cetain
levels limited to specific
discrete values
That means energy levels are
quantized
3 4 ex
13GeV
el
PHY71
Energy Levels
h 6 6 10 34
−13.6 ()
!! =
C 3 108 m s *"
FE
hf = E2 - E1
f
!# = −13.6 ()
Ei - E f
f =
h !" = −3.4 () IE
2 93
!$ = −1.51()
11
If an electron has moved from 3rd
!
f= energy level to the first level it will
"
E.IO emit energy as electromagnetic
wave, what is the frequency of this
wave ? What is the wavelength ?
Ei Ef
151 13 6 s
10 J
PHY71
12 09 ev x 1519 1 9344
Iev 1 6 15195
if an electron move
4 to n 3
from n
what is the
emitted
Energy
freq En 1
E hf
X
E
4 6 63 1534
1 Slev
C 3 108 m s
E3
Ey 0 85 eV
Gs Ey 0.66 ev
0 66 1 6 1519
DE EEE
1.59 104
x
1 88 10
difference between ground state and
m
excited state.
•Normally, electrons occupy the lowest energy level available. This is known as the
ground state.
•Electrons can gain energy and move up the energy levels if it absorbs energy either
by:
o Collisions with other atoms or electrons
o Absorbing a photon
o A physical source, such as heat
•This is known as excitation, and when electrons move up an energy level, they are
said to be in an excited state.
•If an electron gains enough energy to be removed from the atom entirely, this is
known as ionization.
•When an electron returns from a higher excited state to a lower energy state, it
releases energy in the form of a photon.
PHY71
atomic spectra provides evidence for
the quantization of energy in atoms.
•Atomic spectra show the spectrum of discrete wavelengths emitted or
absorbed by a specific atom.
•Photon energy is related to frequency and wavelength by: # = h$.
Therefore, photons with discrete wavelengths have discrete energies
equal to the difference between two energy levels or: #i − #f = h$.
•Photons arise from electron transitions between energy levels.
•This happens when an electron is excited or de-excited from one
energy level to another, by either emitting or absorbing light of a
specific wavelength.
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The energy of the emitted or
absorbed photon
wavelength of the emitted or absorbed radiation and
the energy difference between the energy levels are
related .
• The energy of the emitted or absorbed photon is
given by: ∆" = " − " = h#
• Using the wave equation, the wavelength of the
emitted or absorbed radiation can be related to the
energy difference by the equation:
• This equation shows that the learger the differnce in
energy of the two levels ∆", the shorter the
wavelength
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$ and vice versa.
Atomic Transitions
ME
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Absorbtion
Atomic Transitions
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Atomic Transitions
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Atomic Transitions and Lasers
DE 6.63
1034
h
c 34108ms
1519
e 1 6
ev
En
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The atomic or line spectra.
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The atomic or line spectra.
•Line spectra is a phenomenon that occurs when
excited atoms emit light of certain wavelengths
which correspond to different colors.
•This comes from differences in discrete energy
levels when electrons move between energy levels
within an atom.
•The emitted light can be observed as a series of
coloured lines with dark spaces in between.
•These series of coloured lines are called line or
atomic spectra.
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Atomic Spectra
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Atomic Spectra
Use the below formula to find
the energy for each color
!"
E=
#
J ev
1.6 15 Ere e
3 10 195 1.891
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Atomic Spectra
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Atomic Spectra
Each element produces a unique set of
spectral lines.
•No two elements emit the same set of spectral lines, therefore,
elements can be identified by their line spectrum.
•There are two types of line spectra: emission spectra and
absorption spectra
PHY71
Atomic Spectra
Each element produces a unique set of
spectral lines.
•No two elements emit the same set of spectral lines, therefore,
elements can be identified by their line spectrum.
•There are two types of line spectra: emission spectra and
absorption spectra
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emission spectra and how they are
created.
•For example, if a potential difference is applied between the electrodes in glass tube
filled with a particular gas, the color of the light emitted depends on the gas inside tube.
•The light analyzed using a spectrometer show discrete bright lines, each having a
different wavelength. Such a series of spectral lines is called as emission spectra.
•When an electron transitions from a higher energy level to a lower energy level, this
results in the emission of a photon.
•Each transition corresponds to a different wavelength of light and this corresponds to a
line in the spectrum.
•The resulting emission spectrum contains a set of discrete wavelengths, represented by
coloured lines on a black background.
•Each emitted photon has a wavelength which is associated with a discrete change in
•energy, according to the equation:
•∆!=h-= hc/.
•Therefore, this is evidence to show that electrons in atoms can only transition between
discrete energy levels.
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absorption spectra and how they are
created.
•An atom can be raised to an excited state by the absorption of a photon.
•When white light passes through a cool, low pressure gas it is found that light of
certain wavelengths are missing. This type of spectrum is called an absorption
spectrum.
•An absorption spectrum consists of a continuous spectrum containing all the
colours with dark lines at certain wavelengths.
•These dark lines correspond exactly to the differences in energy levels in an atom.
•When these electrons return to lower levels, the photons are emitted in all
directions, rather than in the original direction of the white light. Therefore, some
wavelengths appear to be missing.
•The wavelengths missing from an absorption spectrum are the same as their
corresponding emission spectra of the same element.
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Hydrogen Atom
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Hydrogen Atom
(sets or families of lines)
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Hydrogen Atom
(sets or families of lines)
Each element will have several series with electrons able to jump between specific
energy levels producing specific energy photons.
•The Lyman series converges on the ground state n = 1 for electrons.
o The Balmer series converges on the second energy level n = 2
o The Ritz - Paschen converges on the third energy level n = 3 and so
on.
•The Lyman series photons will have the most energy since they have
the shortest wavelength.
•The Pfund series photons will have the least energy since they have
the longest wavelength.
•The discovery of these electron jumps helped scientists to understand
how the movement of electrons is able to produce photons of specific
wavelength and energy.
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The Bohr Model
13.6
En = - 2 eV
n
E2 = E1 /4 = -3.40 eV
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The Exclusion Principle
and the Periodic Table
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The Exclusion Principle
and the Periodic Table
He: 1s 2
Ne: 1s 2 2 s 2 2 p 6
PHY71 Ar: 1s 2 2 s 2 2 p 6 3s 2 3 p 6
The Exclusion Principle
and the Periodic Table
Alkali metals Halogens
Li: 1s 2 2 s1 F: 1s 2 2 s 2 2 p 5
Na: 1s 2 2 s 2 2 p 6 3s1 Cl: 1s 2 2 s 2 2 p 6 3s 2 3 p 5
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K: 1s 2 2 s 2 2 p 6 3s 2 3 p 6 4 s1 Br: 1s 2 2 s 2 2 p 6 3s 2 3 p 6 4 s 2 3d 10 4 p 5
Atomic Transitions and Lasers
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