Download Lesson 3 Atomic spectra and the Bohr model

Topic 13
Quantum and Nuclear physics
Atomic spectra and atomic energy states
How do you excite an atom?
1. Heating to a high
temperature
2. Bombarding with
electrons
3. Having photons
fall on the atom
I’m excited!
Atomic spectra
When a gas is heated to a high
temperature, or if an electric current is
passed through the gas, it begins to glow.
Light emitted
cathode
Low pressure gas
anode
electric current
Emission spectrum
If we look at the light emitted (using a
spectroscope) we see a series of sharp
lines of different colours. This is called an
emission spectrum.
Absorption Spectrum
Similarly, if light is shone through a cold gas,
there are sharp dark lines in exactly the same
place the bright lines appeared in the
emission spectrum.
Light
source
gas
Some wavelengths missing!
Why?
Scientists had known
about these lines
since the 19th century,
and they had been
used to identify
elements (including
helium in the sun), but
scientists could not
explain them.
Rutherford
At the start of the 20th
century, Rutherford
viewed the atom
much like a solar
system, with electrons
orbiting the nucleus.
Rutherford
However, under
classical physics, the
accelerating electrons
(centripetal
acceleration) should
constantly have been
losing energy by
radiation (this
obviously doesn’t
happen).
Radiating energy
Niels Bohr
In 1913, a Danish
physicist called Niels
Bohr realised that the
secret of atomic
structure lay in its
discreteness, that
energy could only be
absorbed or emitted
at certain values.
At school they
called me
“Bohr the
Bore”!
The Bohr Model
Bohr realised that the
electrons’ angular
momentum is an
integral (whole
number) multiple of
the unit h/2π. This
meant that the
electron could only be
at specific energy
levels (or states)
around the atom.
The Bohr Model
We say that the
energy of the electron
(and thus the atom)
can exist in a number
of states n=1, n=2,
n=3 etc. (Similar to
the “shells” or
electron orbitals that
chemists talk about!)
n=1
n=2
n=3
The Bohr Model
The energy level diagram of the hydrogen
atom according to the Bohr model
Energy
eV
0
High energy n levels are very
close to each other
n=5
n=4
n=3
n=2
Electron can’t have less
energy than this
-13.6
n = 1 (the ground state)
The Bohr Model
An electron in a higher state than the ground state is
called an excited electron. It can lose energy and end
up in a lower state.
Energy
eV
0
High energy n levels are very
close to each other
n=5
n=4
Wheeee!
n=3
n=2
-13.6
n = 1 (the ground state)
Atomic transitions
If a hydrogen atom is in an excited state, it can make a transition to
a lower state. Thus an atom in state n = 2 can go to n = 1 (an
electron jumps from orbit n = 2 to n = 1)
Energy
eV
0
n=5
n=4
Wheeee!
n=3
electron
n=2
-13.6
n = 1 (the ground state)
Atomic transitions
Every time an atom (electron in the atom) makes a transition, a
single photon of light is emitted.
Energy
eV
0
n=5
n=4
n=3
electron
n=2
-13.6
n = 1 (the ground state)
Atomic transitions
The energy of the photon is equal to the difference in energy (ΔE)
between the two states. It is equal to hf. ΔE = hf
Energy
eV
0
n=5
n=4
n=3
electron
n=2
ΔE = hf
-13.6
n = 1 (the ground state)
The Lyman Series
Transitions down to the n = 1 state give a series of
spectral lines in the UV region called the Lyman series.
Energy
eV
0
n=5
n=4
n=3
n=2
-13.6
n = 1 (the ground state)
Lyman series of spectral lines (UV)
The Balmer Series
Transitions down to the n = 2 state give a series of
spectral lines in the visible region called the Balmer
series.
Energy
eV
0
n=5
n=4
n=3
n=2
Balmer series of spectral
lines (visible)
-13.6
n = 1 (the ground state)
UV
The Pashen Series
Transitions down to the n = 3 state give a series of
spectral lines in the infra-red region called the Pashen
series.
Energy
eV
0
n=5
n=4
n=3
Pashen series (IR)
n=2
visible
-13.6
n = 1 (the ground state)
UV
Emission Spectrum of Hydrogen
The emission and absorption spectrum of hydrogen is
thus predicted to contain a line spectrum at very
specific wavelengths, a fact verified by experiment.
Which is the emission spectrum and which is the
absorption spectrum?
Pattern of lines
Since the higher states are closer to one another, the wavelengths
of the photons emitted tend to be close too. There is a “crowding” of
wavelengths at the low wavelength part of the spectrum
Energy
eV
0
n=5
n=4
n=3
n=2
Spectrum produced
-13.6
n = 1 (the ground state)
Limitations of the Bohr Model
1. Can only treat atoms or ions with one
electron
2. Does not predict the intensities of the
spectral lines
3. Inconsistent with the uncertainty principle
(see later!)
4. Does not predict the observed splitting of
the spectral lines
The “electron in a box” model!
Hi! I’m
Erica
the
electron
☺
The “electron in a box” model!
• Imagine an electron is confined within a
linear box length L.
☺
L
The “electron in a box” model!
• According to de Broglie, it has an
associated wavelength λ = h/p
☺
L
The “electron in a box” model!
• Imagine then the electron wave forming a
stationary wave in the box.
L
The “electron in a box” model!
• Therefore we have a stationary wave with
nodes at x = 0 and at x = L (boundary
conditions)
L
The “electron in a box” model!
• The wavelength therefore of any stationary
wave must be λ = 2L/n where n is an
integer.
L
The “electron in a box” model!
• The momentum of the electron is thus
• P = h/λ = h/2L/n = nh/2L
The “electron in a box” model!
• The kinetic energy is thus = p2/2m =
(nh/2L)2/2m = n2h2/8mL2
The “electron in a box” model!
• Ek = n2h2/8mL2
☺
L
Energy states
This can be thought
of like the allowed
frequencies of a
standing wave on a
string (but this is a
crude analogy).
Erwin Schrödinger
The many problems
with the Bohr model
were corrected by
Erwin Schrödinger, an
Austrian physicist.
d2Ψ/dx2 = -8π2m(E – V)Ψ/h2
The Schrödinger equation
I like cats!
Erwin Schrödinger
Schrödinger
introduced the wave
function, a function of
position and time
whose absolute value
squared is related to
the probability of
finding an electron
near a specific point
in space and time.
I don’t believe
that God
plays dice!
Erwin Schrödinger
In this theory, the
electron can be
thought of as being
spread out over a
large volume and
there are places
where it is more likely
to be found than
others! This can be
thought of as an
electron cloud.
Rubbish!
Wave function
Ψ = (2/L)½(πnx/L) where n is the state, x
is the probability of finding the electron
and L is the “length” of the orbital.
From this we also get the energy to be
EK = h2n2/8meL2
Beware!
I’m used to the
idea of waves, so
I like using
Schrödinger’s
model
This wave function is only a
mathematical model that fits very well. It
also links well with the idea of wave
particle duality (electron as wave and
particle).
But it is only one mathematical model of
the atom. Other more elegant
mathematical models exist that don’t
refer to waves, .but physicists like using
the wave model because they are
familiar with waves and their equations.
We stick with what we are familiar!
Heisenberg Uncertainty Principle
Heisenberg Uncertainty Principle
• It is not possible to measure
simultaneously the position AND
momentum of a particle with absolute
precision.
ΔxΔp ≥ h/4π
Also ΔEΔt ≥ h/4π
That’s it for Quantum physics!
Next week we’ll be looking at
nuclear physics!
Let’s try some questions.