Quanta to QuarksFocus Area 1

This is how some feel….but we

won’t!

Light (Again)

Isaac Newton first showed that white light was made up of all the colours of the visible light spectrum by shining a ray of white light through a glass prism.

In 1801 William Wollaston repeated the experiment using sunlight and found that there were narrow dark bands in the solar spectrum.

These were investigated further by Fraunhofer using his new invention, the spectroscope, in 1814. Fraunhofer found 574 dark lines, which became known as Fraunhofer lines.

Spectral lines were studied further throughout the nineteenth century, most significantly by Gustav Kirchhoff who formulated the three laws of spectroscopy.

Kirchhoff’s laws describe the three situations by which spectra are produced and the spectra that are produced by them. They are:

1. A hot solid body (or a hot dense gas) produces a continuous spectrum. This is the spectrum first described by Newton and can be seen in a rainbow.

2. A hot gas under low pressure produces an emission spectrum. An emission spectrum appears as a number of distinct narrow lines on a black background.

3. A cool gas under low pressure produces an absorption spectrum when a continuous spectrum of light passes through it. An absorption spectrum appears as a continuous spectrum interrupted by narrow dark lines. Wollaston and Fraunhofer observed an absorption spectrum when they examined the spectrum of sunlight.

We need to remember that by the end of the 1800s, people still had no idea what caused these spectral lines.

EXP: Hydrogen Spectra

History of the atom (Brightstorm video)

http://youtu.be/gT6nsloIRa8

Thomson’s Atomic ModelWith the discovery if the electron in 1897, Thompson proposed a model of the atom known as the 'plum pudding model'.

In this model, the atom was composed of electrons (which Thomson still called corpuscles), surrounded by a soup of positive charge to balance the electrons' negative charges, like negatively-charged "plums" surrounded by positively-charged "pudding".

The next big thingThe next major advance in our understanding of the atom came in 1909, as a result of an experiment conducted by Hans Geiger and Ernest Marsden.

Geiger and Marsden were students of Ernest Rutherford, who himself had been a student of Thomson’s.

Geiger and Marsden used alpha particles to examine the distribution of charge in an atom.

They used a thin piece of gold foil as their target, which they surrounded by a circular sheet of zinc sulfide.

The alpha particles illuminated the zinc sulfide when they struck it.

This allowed Geiger and Marsden to measure the deflection of the alpha particles by the atoms in the gold foil.

PhET: Rutherford scattering jar

Geiger and Marsden expected that any deflection detected would be small as the positive charge was distributed evenly throughout the atom in Thomson’s model.

However, their actual results were most unexpected. They found that most alpha particles were not deflected at all, but of those that were deflected, some were deflected by much more than 90°, and some were even deflected 180°.

Rutherford realized that this result could not have been produced if positive charge in an atom was diffuse.

Therefore, the positive charge in an atom must be concentrated in a volume much smaller than the whole atom. (He first used the word ‘nucleus’ in 1912).

Rutherford’s Atom

http://youtu.be/FfY4R5mkMY8

A new modelRutherford used the results of the gold foil experiment to develop his own model of the atom.

The Rutherford model consisted of a massive, positively charged nucleus surrounded by a cloud of negatively charged electrons.

The vast majority of the volume of Rutherford’s atom was empty space.

Rutherford’s model fitted the experimental data of both Thomson’s experiment and the Geiger-Marsden experiment.

The Rutherford model was a great step forward in our understanding of atomic structure but it still had its limitations.

To overcome for force of attraction between the positive nucleus and the electrons, electrons must be in circular motion (much like the planets around the Sun).

Since electrons were in circular motion, they would be experiencing acceleration and accelerating charges were known to emit electromagnetic radiation.

This loss of energy would cause the electrons to spiral closer to the nucleus (like orbital decay for satellites) and matter would be destroyed.

This was clearly not happening so there were problems with the model.

Back to HydrogenWhen hydrogen gas is excited by a large potential difference, it produces the characteristic emission and absorption spectra.

A series of spectral lines that were found in the visible light section of the electromagnetic spectrum were called the Balmer series.

Spectral lines were also found to exist in other sections of the EM spectrum and these were given other names.

Rutherford's model could not explain spectral lines either.

As electrons spiralled toward the nucleus with increasing speed, they should emit radiation of all frequencies, not just the one frequency corresponding to the wavelength of the spectral line.

Thus, the observed spectrum of the element should have been continuous and not a line spectrum.

Now what?By the turn of the 20th Century physicists understood the conditions by which hydrogen’s spectral lines were produced and the mathematical relationship that determined the wavelength of the spectral lines.

In 1885 Johann Balmer published a mathematical equation that correctly predicted the wavelength of the lines in the hydrogen spectra:

where h = 3.6456 × 10-7 m, and m is an integer greater than 2. Substituting m = 3, 4, 5, and 6, Balmer was able to calculate the wavelength of hydrogen’s spectral lines.

Balmer did not propose an explanation of why spectral lines were produced. He simply examined the data and found a mathematical relationship that described it.

Three years later Johannes Rydberg modified Balmer’s equation. Rydberg’s equation was:

where R = 1.097 × 107 m, and n1 and n2 are both integers with n1<n2 . Balmer’s equation is a special case of Rydberg’s equation where n2 = 2. Because of this, the spectral lines described by substituting n2 = 2 into Rydberg’s equation are known as the Balmer series.

So the spectral lines were now mathematically understood, however there was no theory explaining why atoms produced emission and absorption spectra.

This was one of the great successes of the Bohr model.

Bohr’s Atom

http://youtu.be/hpKhjKrBn9s

This is not Bohr-ing

In 1913 Bohr produced a model of the atom that both dealt with the problems of the Rutherford model and explained atomic spectra.

Bohr examined evidence collected by other scientists and recognised the connection between Balmer, Planck and Einstein.

He combined their ideas and predicted that Planck’s blackbody oscillators were electrons, that quanta were involved with electrons transferring from one energy level to another, and that it was these quanta which determined spectra.

Bohr’s Postulates

Electrons revolve only in certain “allowed” orbits. Bohr theorised that there are a series of orbits, at fixed distances from the nucleus, in which an electron will not constantly emit radiation as demanded by classical theory.

2. Electrons gain or lose energy to “jump” between orbits. To jump up to a higher orbit, an electron must gain a certain quantity of energy. If it drops back to lower orbit, it must emit that exact same amount of energy.

These quantities of energy are “quantised”, so each orbit is really a “quantum energy level” within the atom.

The amount of energy absorbed or emitted during a “jump” is defined by Planck’s Equation E = hf, and the corresponding wavelengths of light are defined by the Rhydberg Equation. The integer numbers nf and ni turn out to be the “quantum numbers” of the orbits, counting outwards from the nucleus.

The energy that is absorbed or released as electrons move between energy levels explains why elements emit and absorb radiation of specific wavelengths.

The energy levels for all the hydrogen atoms in a sample of hydrogen gas are identical.

When an electron in the second energy level absorbs a photon of the right wavelength it will gain the energy it needs to move into the third energy level.

Therefore, photons at this wavelength will be absorbed by the electrons in the second energy level and will not be transmitted through the hydrogen.

This wavelength will be omitted and a black line will appear in the absorption spectrum.

When an electron in the second energy level emits a photon of the right wavelength it will move into the first energy level.

The photons emitted will appear as a line in the emission spectrum of hydrogen.

Rydberg’s equation relates the wavelength of the photons to the changes in energy level of the electrons. Therefore, it can be rewritten as

where ni indicates the initial energy level of the electron and nf indicates the final energy level of the electron.

In fact, all spectral lines for hydrogen can be explained in this way.

Back to Hydrogen (Again)

Bohr’s explanation of the Balmer series was that if an electron fell from a higher shell down to shell 2, the spectrum emitted was known as the Balmer series.

The Balmer series was in the visible spectrum. There are names given to the spectra when electrons fall from higher shells down to each of the shells.

For example, when electrons fall to the first shell the spectrum emitted is known as the Lyman series which is in the ultraviolet spectrum.

Summary: Bohr’s Postulates

1 Electrons exist in stable orbits. An electron can exist in any of several special circular orbits with no emission of radiation. These orbits are called stationary states.

2 Electrons absorb or emit specific quanta of energy when they transition between stationary states (orbits). In contradiction to classical electromagnetic theory, a sudden transition of an electron between two stationary states will produce an emission or absorption of quantised radiation (a photon), described by the Planck–Einstein relation.

3 Angular momentum of electrons is quantised. An electron in a stationary state (orbit) has a quantised angular momentum that can take only values of

where n is the principal quantum number.

Questions on Rydberg

Nothing’s PerfectThe Bohr model was clearly a step towards an accurate atomic model and not a completely accurate model in itself.

It was limited in its application, contained inconsistencies, and could not explain some phenomena.

The Bohr model of the atom was specifically developed with hydrogen in mind; it succeeded in explaining the hydrogen spectrum. However, when it was used to try to explain the spectra of·other elements several problems emerged.

The primary reason was that hydrogen has only one electron orbiting the nucleus (in its neutral form). All other elements have multiple electrons orbiting the nucleus (when they are neutral).

As all electrons are negative the electrons repel each other. In larger atoms an effect known as 'screening' occurs. The inner electrons screen the outer electrons from the positively charged nucleus.

As a result, the outer electrons do not feel all the positive charge. The Bohr model does not take into account this interaction and so cannot predict the spectral lines of large atoms with many electrons.

The Bohr model also cannot predict or explain the relative intensity (brightness) of spectral lines.

There are several laws in quantum mechanics that forbid certain transitions between orbits. Rules known as the selection rules allow certain transitions to go ahead but forbid or suppress others.

The allowed transitions showed up in spectra with brighter or more intense spectral lines and at the time, this could not be explained by the Bohr model as the selection rules were not known.

Bohr was also unable to predict the hyperfine structure seen in atomic spectra, even for hydrogen.

Hyperfine spectral lines are faint, thin lines that exist as a cluster around a main spectral line.

This splitting of the spectral lines comes about because of the interaction between the angular momentum of the protons and the electrons.

Bohr did not know this at the time so the model could not explain these spectral observations.

As the electrons circulate the nucleus they create a magnetic field. Any moving charge creates a magnetic field.

When an external magnetic field is applied to the atom this adds to the magnetic field caused by the motion of the electrons.

The interaction of the electron with this altered magnetic field produces a different energy to that produced when the external magnetic field is turned off.

This changes the spectrum produced by the atom by causing the spectral lines to split in the presence of an external magnetic field (known as the Zeeman effect). Bohr did not consider atoms and their magnetic fields in his model.

End of Focus Area 1