Download Bohr`s Model of the Atom

History of the Atomic Model
Bohr’s Model
of the Atom
• Democritus (400 B.C.)
• Believed that matter was composed of
invisible particles of matter he called
atoms.
• Antoine Lavoisier (1700’s)
• Law of Conservation of Mass – Matter
is not created or destroyed.
Niels Bohr (1923) was the first to propose that
the periodicity in the properties of the elements
might be explained by the electronic structure of
the atom
• Joseph Proust (1700’s)
History of the Atomic Model
History of the Atomic Model
• Law of constant composition –
compounds are composed of atoms in
definite ratios.
• Marie Curie (1898)
• John Dalton (Late 1700’s)
• Studied uranium and thorium and called
their spontaneous decay process
"radioactivity,” leading Rutherford to
discover the alpha particle.
• First atomic theory explaining chemical
reactions
• Henri Bacquerel (1896)
• Hantaro Nagaok (1903)
• While studying the effect of x-rays on
photographic film, he discovered some
chemicals spontaneously decompose and
give off very penetrating rays.
• Postulated a "Saturnian" model of the
atom with flat rings of electrons revolving
around a positively charged particle.
• Robert Millikan (1909)
• J.J. Thomson (1897)
• Found the charge and mass of the electron
in his famous “oil-can” experiment.
• Discovered the electron using cathode
ray tubes
History of the Atomic Model
• Ernest Rutherford (1911)
• Discovered the nucleus in his famous
“gold foil” experiment.
• Data from his experiments led
Rutherford to propose a planetary
model in which a cloud of electrons
surrounded a small, compact nucleus
of positive charge. Only such a
concentration of charge could produce
the electric field strong enough to cause
the heavy deflection of alpha particles
observed.
Rutherford's Problems
1.
according to the Larmor
Formula in classical
electromagnetism; an
orbiting charge should
steadily lose energy and
spiral toward the nucleus,
colliding with it in a small
fraction of a second.
2.
the planetary model could not
explain emission and
absorption spectra of atoms
that were observed.
History of the Atomic Model
• Niels Bohr (1913)
• Solidified Rutherford’s Planetary atomic
model by using the work of Max Plank
and Albert Einstein on the nature of
Electromagnetic Radiation to predict the
spectral lines of hydrogen described by
the work of Johann Balmer and
Johhanes Rydberg.
The Emission Spectra of Elements
• One property of the elements
that really captured the
attention of scientists is that one
does not observe a continuous
spectrum for hydrogen, as one
gets from a white light source.
• Only a line spectrum of discrete
wavelengths is observed.
To develop an understanding of Bohr’s Planetary
Model, we must investigate the nature of
Electromagnetic Waves and the work of a few
important scientists.
History of the Atomic Model
• Johann Balmer (1885)
• Showed that the wavelengths of the four
visible lines of hydrogen fit a simple
formula relationship.
λ = hm2/(m2 - n2)
History of the Atomic Model
• Johannes Rydberg (1888)
• Expanded Balmer’s relationship to a more
general equation that could be used to
calculate all spectral lines of hydrogen,
not only the visible. This relationship
eventually grew into what is known as the
Rydberg equation:
1
1 1
 (R H ) 2  2 
λ
 n1 n 2 
RH = Rydberg constant
= 1.096776 x107 m-1
n
= principle Quantum Number
Electromagnetic Waves
•Electromagnetic Radiation refers to energy
that travels though space consisting of an
energy wave and a perpendicular magnetic
wave.
Waves
• The distance between corresponding
points on adjacent waves is the
wavelength ().
Waves
• The number of waves
passing a given point per
unit of time is the
frequency ().
• All transverse waves fit
the inverse proportion:
• Describes all wavelengths of electromagnetic
radiation.
• Visible light only makes up a small portion of the
electromagnetic spectrum
νλ = k
:
cycles
 sec 1  Hertz (Hz)
sec
History of the Atomic Model
• Max Plank (1900)
• Studying energy absorbed and emitted
by hot glowing matter, He noted that
energy is only released or absorbed in
“chunks” of some minimal size he
called quanta.
Quanta = minimal
amount of energy that
can be emitted or
absorbed by
electromagnetic
radiation.
History of the Atomic Model
• Albert Einstein (1905)
• By observing the Photoelectric effect,
Einstein proposed that a beam of light is
not a wave propagating through space,
but rather a collection of discrete wave
packets(photons), each with energy hf.
• This shed light on the previous discovery
of the Planck relation (E = hν) linking
energy (E) and frequency (ν) as arising
from quantization of energy. The
factor h is known as the Planck constant.
Plank’s Quantization of EMR
E = hν
E = energy
h = Planck’s constant
= 6.626 x 10- 34 J. s
ν= frequency
So, energy is absorbed or emitted in
packets, or quanta, of:
hν, 2h ν, 3h ν, 4hν...
Equation sheet
The Photoelectric Effect
• In opposition to Maxwell's theory that EMR energy is
proportional to intensity, Einstein concluded that
EMR energy is proportional to wave frequency:
Ephoton = h
where h is Planck’s constant
(6.63  10−34 J-s.)
Einstein's Wave-Particle Duality of Light
Albert Einstein determined that E.M.R. is
composed of packets of quantized energy called
photons; each having its own characteristic
wavelength and traveling at a constant speed,
the speed of light (c), 3.00 X 108 m/s.
• Therefore, if one knows the wavelength of light, one
can calculate the energy of one photon-wave, or quanta,
of that light:
c = 
E = h
Reminder
1J  1
kg  m 2
s2
So:
Short wavelength -->
high frequency
high energy
Long wavelength -->
small frequency
low energy
Bohr’s Model
•
Bohr solidified Rutherford’s planetary model
of the atom by explaining how electrons
maintain specific energy levels orbiting the
nucleus in particular circular orbits with
fixed energy, its distance from the nucleus
being proportional to its energy.
• Under this model an electron could not spiral into the
nucleus because it could not lose energy in a
continuous manner; instead, it could only make
instantaneous "quantum leaps" between the
fixed energy levels. When this occurred, light was
emitted or absorbed at a frequency proportional to
the change in energy (hence the absorption and
emission of light in discrete spectra).
1
1 1
 (R H ) 2  2 
λ
 n1 n 2 
•
c = 
E = h
According to Bohr, the energy of these
quantized states can be determined by:
En= - hcRH 1/n2
Or:
En= - k 1/n2
En
RH
= Energy in a main energy level
= Rydberg constant
= 1.096776 x107 m-1
k
= hcRH
= 2.179 x 10-18 J
n = principle Quantum Number
Bohr’s Model
1. Electrons in an atom can only
occupy certain orbits
(corresponding to certain
energies).
2. Electrons in permitted orbits
have specific, “allowed”
energies; these energies will not
be radiated from the atom.
These “allowed” energy levels (En or n)
can have quantized values from 1 to
infinity (∞)
Or by rearranging:
En =
-2.18 x 10-18 J
n2
Lower the Energy (more -), the
more stable and visa versa.
Bohr’s Model
3. Energy is only absorbed or
emitted in such a way as to
move an electron from one
“allowed” energy state to
another; the energy is defined
by:
Ephoton = hν
1. Electrons exist in
the lowest
energy level
possible, their
ground state.
2. As Energy is absorbed by the atom, electrons
are ejected to outer electron orbits of higher
energies known as excited states
3. Excited states are unstable, therefore,
electrons will “fall” back to their ground states,
releasing quantum(s) of energy called photons.
• For the transition of an e- from an initial
energy level (Ei) to a final energy level (Ef), we
can write:
Substituting into the equation:
ΔE = Enf – Eni = Ephoton
• The absorbed energy is equal to the change in
energy states for an electron; which is equal to
the energy of an absorbed or released photon.
And rearranging, we get:
ΔE = Enf – Eni = Ephoton
 1
1
ΔE electron  E photon   k 

2
n 2
n
i
 f
• Where:
ΔEelectron = Ephoton = h
=c/
Using the Bohr
model, we can
calculate the
wavelengths
absorbed or emitted
from a Hydrogen
atom.
Likewise, we
can calculate the
energy level jumps
of a Hydrogen
electron that has
absorbed energy.
remember:
ΔE = h 
=c/




Know
These !!
1.Calculate the energy required to
excite the hydrogen electron
from level n=1 to level n=2.
Also, calculate the wavelength of
light that must be absorbed by a
hydrogen atom in its ground
state to reach this excited state.
2.Calculate the energy required to
remove the electron from a
hydrogen atom in its ground
state.
History of the Atomic Model
• Henri Mosely (1915)
• Determined the charges on the nuclei of
most atoms resulting in a reorganization
of the periodic table based upon atomic
number instead of atomic mass.
• Ernest Rutherford (1917)
• concluded that hydrogen nuclei were
singular particles and a basic constituent
of all atomic nuclei. He named such
particles protons.
Bohr’s Model
•
Bohr’s theory was a great accomplishment and he
Received the Nobel Prize in 1922.
• However, Bohr's model was not perfect.
 It could only predict the spectral lines of
hydrogen; it couldn't predict those of multielectron atoms.
 Worse still, as spectrographic technology
improved, additional spectral lines in hydrogen
were observed which Bohr's model couldn't
explain.
Bohr’s quantized energy state was then
corrected to take into the account the
effect of multiple proton nuclei:
z2
E   hcRH 2
n
where:
z = nuclear charge
k = hcRH = +2.179 x 10-18 joule
Remembering that for Hydrogen, z = 1.