Science, Technology and Environment
Laboratory,
Pedagogical Department P.E.,
University of Athens, Greece
Hands-on spectrum lines – Introducing microscopic
quantum explanations of the emitted photons to
non-physics major’s students
Vassilis Dimopoulos, George Kalkanis
The Contents
mechanic
waves
duality of
light/electron
early models
of atom
spectrum
quantum model for the
atom of hydrogen
A spectroscope is used in order to observe the
continuous and linear spectra of various lights.
Continuous spectrum
Emission line spectrum
The line spectra serves as a key to the structure
of the atom, since any atomic theory must be
able to explain why atoms emit light of discrete
wavelengths and should be able to predict
what these wavelengths are.
2 2

   U  E
2m
ψ(r, θ, φ) = R(r) Θ(θ) Φ(φ)
Some of the wave functions for the atom of Hydrogen:
 100 
 210 
1
a03
1
4 2a03
e
 r / a0
(2 
r r / 2 a0
)e
cos
a0
1
r  r / 2 a0
 200 
( 2  )e
a0
4 2a03
 211 
1
r r / 2 a0
e
sin e i
8 a03 a0
Back
The wavefunction cannot been pictured
The ψ2 is a real number and gives the probability per unit volume that the
particle will be found at any given point. The ψ2 is called the probability
density (Serway, 1986)
In a dot’s representation the value of ψ2 is higher when the density of the
dots is high
The probability density is also called electronic density or electronic cloud
Back
We can use the radial probability distribution in order to
calculate the probability of finding the electron within the
area x < r < y (Serway, 1986).
Having calculated the probability we converse this number
to the frequency of finding the electron in different areas for
each state.
Back
The probability of
finding a sphere /
unit of surface
increases
If we move on a
circle the higher
probability of
finding a sphere is
on a circle of a
specific radius
The representation of ψ2 is different to the representation of P(r)
Back
The representation of ψ2 is different to the representation of P(r)
 100 
1
a03
e  r / a0
Back
The representation of ψ2 is different to the representation of P(r)
 100 
1
a
3
0
e
 r / a0
 200 
1
4 2a03
(2 
r  r / 2 a0
)e
a0
Back
Emphasis is on the microscopic explanation of the spectrum of hydrogen
An energy diagram is used in order to confront that a spectral line can be
created only by transitions between two discrete energy levels