Hands-on spectrum lines – Introducing microscopic quantum explanations of the emitted photons to non-physics major’s

students

Vassilis Dimopoulos, George Kalkanis

Science, Technology and Environment Laboratory,

Pedagogical Department P.E.,

University of Athens, Greece

The ContentsThe Contents

mechanic waves

duality of light/electron

spectrum

early models of atom

quantum model for the atom of hydrogen

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.

A spectroscope is used in order to observe the continuous and linear spectra of various lights.

EUm

22

2

ψ(r, θ, φ) = R(r) Θ(θ) Φ(φ)

Some of the wave functions for the atom of Hydrogen:

0/

30

100

1 area

02/

030

200 )2(24

1 area

r

a

cos)2(24

102/

030

210are

a

r

a

iar eea

r

a

sin

8

102/

030

121

Back

The wavefunction cannot been pictured

Back

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

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).

Back

Having calculated the probability we converse this number to the frequency of finding the electron in different areas for each state.

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

Back

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)

0/

30

100

1 area

Back

The representation of ψ2 is different to the representation of P(r)

0/

30

100

1 area

02/

030

200 )2(24

1 area

r

a

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