Atoms Truc t

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Atomic physics/Atomic structure and quantum

physics

Chan Kee-Lin Steven, [email protected]

March 31, 2002

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1 Models of the atom

Tool: Models of the atomCategory: Atomic physics/Atomic structure and quantum physics

It was Rutherford who initially postulated the basis of todays theory ofatomic structure. He observed that some alpha particles bombarding a thingold foil would be scattered at wide angles while most would pass straightthrough. To Rutherford, this indicated that an atom had most of its andall of its positive charge contained in a very small volume or nucleus. Theelectrons orbited the nucleus but far away enough so that they did notshield the nucleus positive charge. Alpha particle scattering was, therefore,due to electrostatic repulsion.

Later, 2 of Rutherfords assistants, Geiger and Marsden, conducted ex-periments to prove Rutherfords hypothesis. Although there was strongexperimental evidence for a nucleus, the idea that electrons orbited thenucleus did not jive with classical physics. Bohr sought to overcome thisflaw by suggesting that electrons were confined to specific orbits or energylevels.

Any electron in a specific energy level has a fixed amount of kinetic andpotential energy combined. Electrons can change energy levels by absorbingenough energy to jump to a higher level or by releasing enough energy todrop down to a lower one.

In practice, Bohrs model was not perfect and has been superseded by a

quantum mechanical model. However, the idea of energy levels still remainsvery useful.

2 Plancks theory

Tool: Plancks theoryCategory: Atomic physics/Atomic structure and quantum physics

Planck figured out that electromagnetic radiation is emitted as energypackets or quanta of energy (now called photons). Each photons energyis related to the frequency of the generating radiation via the following

equation. E = hf (1)

E is the energy of a photon.h is Plancks constant.f is the frequency of the radiation emitting the photon.

Copyright c March 31, 2002, Keelin ChanAll rights reserved. (www.jcphysics.com)

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His insight has a lot of consequences. For example, acknowledging thatelectromagnetic radiation energy can be contained within discrete packetsis equivalent to saying that light can behave like a stream of particles.

3 Absorption and emission spectra

Tool: Absorption and emission spectraCategory: Atomic physics/Atomic structure and quantum physics

As an electron can only be in specific energy levels in an atom, transi-tion from one level to another can only be achieved by absorbing or emit-

ting the exact difference in energy between levels. This needs to be doneinstantaneously and is most easily accomplished by the electron absorbingor emitting a photon of the correct energy.

Suppose there is a source of electromagnetic radiation which contains allwavelengths. Lets say that the radiation passes through a gas under lowpressure and examined. Certain wavelengths would then be found missingfrom the resultant spectrum. Such a phenomenon is known as an absorptionspectra.

Figure 1: Wavelengths missing from absorption spectra.


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Each missing wavelength actually corresponds to a photon that would

cause an electron to make a unique transition between energy levels. Take,for example, an atom with 4 different energy levels.

level 4

level 3

level 2

level 1

Figure 2: An atom with 4 energy levels.

An electron in level 1 can go to level 2, level 3 or level 4. Similarly,an electron in level 2 can go to level 3 or level 4 etc. In total, there are6 possible transitions and a maximum of 6 missing wavelengths. If therehappens to be 2 or more transitions that share the same difference betweenlevels, then they would account for only 1 missing wavelength.

Heating up a gas will result in the electrons of its constituent atomsentering excited states (higher energy levels). Instead of absorbing photons,these energized electrons emit photons as the drop down to lower energylevels. Visualization of these photons results in an emission or line spectra.

Once again, each of these wavelengths will correspond to a distinct tran-sition of an electron between energy levels.

4 Electron collision experiments

Tool: Electron collision experimentsCategory: Atomic physics/Atomic structure and quantum physics


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Figure 3: Wavelengths present in an emission spectra.

Absorbing and emitting photons isnt the only way for electrons to tran-sition energy levels. They may also absorb the needed energy from collisionwith fast moving free electrons.

One way to illustrate this phenomenon , among other things, is to con-

duct an electron collision experiment. In it, electrons are shot througha low pressure (dilute) gas by means of a potential difference across thechamber.

These fast moving, free electrons can interact with the gas atoms in afew ways:

a. Simply collide with the gas atoms.

b. Collision with an electron bound to a gas atom Just enough energywill be transferred to bring the bound electron to a higher energy level.However, this transition is only momentary (about 1 nanosecond) andthe electron returns to a lower state, emitting a photon in the process.The potential difference (PD) across the chamber of the apparatusat which these transitions are observed is known as the excitationpotential.

c. Increasing the PD increases the kinetic energy of the free electrons.Sometimes, so much energy is transferred to the bound electron that


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transparent gas chamber with low pressure gas

DC power supply

Figure 4: Schematic of an electron collision experiments apparatus.

it escapes from the atom and, itself, becomes a free electron. ThisPD at the point when this occurs is known as the ionization potential.

5 Photo-electric effect

Tool: Photo-electric effectCategory: Atomic physics/Atomic structure and quantum physics

Certain metals emit electrons when their surfaces are exposed to elec-tromagnetic radiation. Such a phenomenon is known as the photo-electriceffect. After much experimentation, a few observational rules have beenobserved.

a. The electron emission rate is proportional to the intensity of the inci-dent radiation.

b. Electrons are ejected with a range of energies. The greater the fre-quency of radiation, the more the maximum speed of emission in-creases.

c. Emission is instantaneous once the frequency of incident radiation isincreased past a certain threshold frequency. Whatever the intensity,there is no emission below this threshold frequency.


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Using Plancks ideas, Einstein formulated a model for photo-electric

emission. He proposed that a minimum amount of energy, known as thework function, is required to liberate an electron from the metal. It followsnaturally that the work function and threshold frequency can be relatedmathematically.

= hf0 (2)

is the work function.h is Plancks constant.f0 is the threshold frequency.

If the incident radiation had a frequency > f0 then all the extra en-ergy absorbed would appear as kinetic energy. Therefore, Einsteins photo-

electric equation ishf = hf0 +

1

2mv2 (3)

f is the frequency of incident radiation.m is the mass of an electron.v is the speed of ejection.

Even in the metal, electrons posses a distribution of kinetic energieswhich directly contributes to ejected electrons having different kinetic ener-gies. The shape of this distribution is dependent on the temperature of themetal.

6 Wave-particle duality

Tool: Wave-particle dualityCategory: Atomic physics/Atomic structure and quantum physics

The photo-electric effect is especially strong evidence for the particulatenature of electromagnetic waves. de Broglie suggested that the converse wasalso true: particles of matter could behave like waves. Integral to this theoryis the idea that a particle moving with a non-zero velocity has an associatedwavelength given by

=h

mv(4)

is the associated wavelength.h is Plancks constant.m is the mass of the particle.v is the velocity of the particle.


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p is the momentum of the photon.

m is the mass of the photon.c is the velocity of light.

To find the photons mass equate Einsteins mass-energy relation withthe energy of a photon.

E = mc2 =hc

mc =h

(7)

E is the energy of a photon.

h is Plancks constant. is the wavelength of the photon.

Simply substitute eqn. (7) into eqn. (6) to obtain the final equation forthe momentum of a photon.

p =h

(8)


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