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9.8 Option- From Quanta to Quarks: 1. Rutherford and Bohr
Extract from Physics Stage 6 Syllabus (Amended
October 2002) © Board of Studies, NSW.
[Edit: 14 Aug 08]
Prior learning: Preliminary modules 8.2, 8.3, 8.4, HSC Module 9.4.
Background: In the early 1900s physics was an active area of research. Scientists were only just beginning to utilise the concept of the major research centre where individuals with great intellect and promise were concentrated to expand the frontiers of science and perform the basic research required to push technology forward. Almost for the first time, being a scientist was a profession. In this environment, exciting discoveries were being made and published on a regular basis.
discuss the structure of the Rutherford model of the atom, the existence of the nucleus and electron orbits
- Rutherford concluded in 1911 that an atom of any element consisted of a tiny positive nucleus with as many positive charges as the atomic number of that element. He also concluded the electrons, that were equal in number to the positive charges in the nucleus, orbited at considerable distance from the nucleus.
perform a first-hand investigation to observe the hydrogen spectrum
- This is best done by passing an electric current through a low pressure hydrogen gas discharge tube and observing with a spectroscope the characteristic Balmer series spectrum in the light energy given out by the excited hydrogen gas atoms. Discuss the method to be used with your teacher.
analyse the significance of the hydrogen spectrum in the development of Bohr’s model of the atom
- The Danish physicist, Niels Bohr, extended
Rutherford's atom model by arranging the electrons in
concentric spherical shells. He proposed that
electrons could orbit the nucleus in a stable manner only
at a few specific distances from the nucleus whereas all
other orbital radii were unstable. Bohr did this after
linking the nature of the spectrum of hydrogen to the
nature of electron orbits around the nucleus. In fact, Bohr
could not have developed his theory of the atom without the
knowledge of the spectrum of hydrogen.
Atoms of a particular element, such as hydrogen, will emit their own unique frequencies of radiation. This is their characteristic spectrum.
Bohr linked these characteristic wavelengths of light emitted from excited hydrogen atoms to being the energy emitted as an electron moved from a higher energy shell to a lower energy shell. He reasoned that since the energy emitted was of characteristic amounts and never in amounts in between, that the stable shells were of specific distances from the nucleus and that electrons could only exist stably at those fixed distances from the nucleus. This analysis becomes very complicated for the elements with more than one electron so it was critical that Bohr used hydrogen as his simplest case then extrapolated his model to the heavier elements with more than a single electron.
process and present diagrammatic information to illustrate Bohr’s findings with the Balmer series
- Refer to and process a number of
diagrammatical representations that illustrate Bohr’s
findings with the Balmer series. Bohr's findings are
generally presented as a series of electron jumps from the
6th, 5th, 4th and 3rd electron orbital to the 2nd electron
orbital out from the nucleus of the hydrogen atom to
produce the four visible emission lines in the spectrum of
hydrogen. These emission lines are called the
Hα, Hβ, Hχ
and Hδ spectral lines.
- Your diagrams should be presented to show the electron jumping from the 6th to the 2nd shell, 5th to the 2nd shell, 4th to the 2nd shell and 3rd to the 2nd shell to produce the four visible light emissions in the Balmer series.
solve
problems and analyse
information using: 
- This equation is the Balmer or Rhydberg equation
depending on the reference used to identify the equation.
It is used to describe the spectrum of discrete wavelengths
of the spectral lines emitted from hydrogen. In the
equation, R is the Rhydberg constant. The value of R is
found on the HSC examination data sheet. For the visible
spectral lines for hydrogen in the Balmer series,
nf is the second stable orbital out from the
nucleus, ni is the orbital the electron starts
from before emitting electromagnetic impulses reaching the
nucleus and is either 6, 5, 4 or 3.
- One of the most common mistakes made by students
applying the equation is that they are asked to calculate
the wavelength, λ ,but the equation as written
provides the inverse of the wavelength. Students substitute
the values into the equation but forget to use the inverse
button on their calculator, so present the reciprocal of
the answer required. Note the Balmer equation applies to
orbital movements that result in wavelengths in the
infrared and UV portions of the electromagnetic spectrum
although the work of Balmer involved only the four visible
spectral lines of the hydrogen spectrum.
- A sample problem might ask for you to determine the wavelength of the shortest spectral line in the visible spectrum of hydrogen. That is produced when an electron jumps down from the 6th to the 2nd orbital. A solution is shown below.
Note that this line is in the violet of the visible spectrum. If an electron were to move from a higher orbital, say 7 or 8 to the 2nd orbital then the emission radiation forming that spectral line would lie in the UV portion of the spectrum. Similarly electrons can move to or from orbitals. When moving to higher energy orbitals they absorb a photon of that wavelength. When moving to lower energy orbitals they emit photons. It is important to recognise that the Balmer equation also applies to electrons moving to orbitals other than the 2nd orbital. The Paschen series involves the movement of electrons from the 6th, 5th and 4th orbital to the 3rd orbital for example. These emissions are in the infrared part of the visible spectrum.
discuss Planck’s contribution to the concept of quantised energy
- Planck is the father of the concept of quantised energy. Planck used the idea of energy in discrete packets or quanta given by the equation E = hf to explain away the nature of radiation emitted from a blackbody. Planck had a traditional view of physics and came up with the idea of quanta to enable his explanation for blackbody radiation to work. He was initially uncertain of the concept's validity.
define Bohr’s postulates
-
Bohr's postulates were:
- Electrons can revolve around the nucleus in certain
metastable orbits without radiating energy or falling
toward the nucleus despite having opposite charges to
the nucleus.
- When an electron moves to a lower energy metastable
state or orbital it emits energy in the form of
electromagnetic radiation given by the relationship E =
hf . If an electron moves to a higher
metastable energy state it must gain a quantity of
electromagnetic energy also given be the equation E =
hf . That is the electrons movement from a
specified higher energy state to a lower energy state
always results in the emission of electromagnetic
radiation of specific frequency being emitted. An
electron moving to a higher specific energy level can
only do so if the electron is able to absorb
electromagnetic energy of a specific threshold
frequency or a higher frequency.
- An electron in a metastable orbit has an angular
momentum that is an integer multiple of
- Electrons can revolve around the nucleus in certain
metastable orbits without radiating energy or falling
toward the nucleus despite having opposite charges to
the nucleus.
describe
how Bohr’s postulates led to the development of a
mathematical model to account for the existence of the
hydrogen spectrum:
- The equation was first developed in another form by
Balmer as an empirical equation to describe the observation
of the visible spectrum of hydrogen produced and observable
when hydrogen gas was excited by the addition of energy.
The equation in the original form was modified by Rhydberg
until it worked and could be applied to explain the
spectrum of hydrogen by using integer values of n, only as
suggested by Bohr in his postulates.
analyse secondary information to identify the difficulties with the Rutherford-Bohr model, including its inability to completely explain:
- the spectra of larger atoms
- the relative intensity of spectral lines
- the existence of hyperfine spectral lines
- the Zeeman effect
- Analyse at least two secondary sources to identify the difficulties with the Rutherford-Bohr model. The following syllabus point provides a sample answer of a discussion of the difficulties.
discuss the limitations of the Bohr model of the hydrogen atom
- The Bohr model was the first and best available at the
time of its conception. It largely explained the
unexplainable observations at the time for the behaviour of
the simplest atom known, hydrogen and stood as the base for
further work by Bohr and others that extended our
understanding of the nature of matter. The Bohr model did
have some serious limitations in what it could
satisfactorily explain.
- The Bohr model of the atom was able to be exclusively
applied to hydrogen. It simply couldn't explain the
behaviour of atoms with more than one electron.
- The Bohr model was unable to explain the observed fact
that some spectral lines were more intense than others in
the spectrum of hydrogen.
- When the individual spectral lines were examined
closely it was found that they were not solid lines of
emitted light or a narrow range of frequencies emitted from
the atom but that they were in fact made up of a number of
hyperfine spectral lines. This could not be explained by
the Bohr model of the atom.
- The Bohr model was at a loss to explain the observation that when a discharge tube was placed in a magnetic field the spectral lines were split into several finely separated but individual lines (the Zeeman effect). This implied the energy levels were split which was unacceptable to the concept of stable orbitals or energy levels in the Bohr model.
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