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Atomic Physics Project

Chapter 15

Becca E

on 4 January 2013

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Transcript of Atomic Physics Project

Bohr Dalton Millikan Quantum Model Rutherford Thomson Progression of Atomic Theories 1803 1898 1909-1911 1913 1924 Thomson's model is called the "Raisin-bun Model" because he suggested that an atom may consist of electrons lodged in a mass-less positive body - looking a bit like
raisins embedded in a blob of dough. It is
also called the "Plum Pudding Model". Negative electrons embedded in a positive body Limitations His model attributed that mass was evenly spread out throughout the atom (due to the even spacing of protons and electrons), therefore he could not explain Rutherford's conclusion that mass is concentrated in the centre while the electrons orbit around the nucleus. Also, Thomson's model could not explain radioactivity or atomic spectra. 1909 Advancements Thomson discovered the electron, which was a huge step up from Dalton's solid sphere. He measured the deflection of a cathode ray accelerated through a potential difference to determine a charge-to-mass ratio. He realized that the electrons deflected towards the positive plate so he knew that it was a negative particle. It was later given the name "electron". Solid, hard Sphere Dalton developed an atomic theory to explain the ratios in which elements combine to form compounds. Dalton's depiction of the atom is a hard sphere like a billiard ball. His theory is a cornerstone upon which modern atomic theory is based. Dalton stated that:
All matter is composed of atoms
Atoms cannot be made or destroyed
All atoms of the same element are identical
Different elements have different types of atoms
Chemical reactions occur when atoms are rearranged
Compounds are formed from atoms of the constituent elements
Although modern atomic theory has progressed and been modified, the essence of Dalton's theory remains accurate. The atom Sources

http://www.physicssource.ca/index2.html (chapter 15)
http://www.preservearticles.com/201012281847/postulates-and-limitation-of-daltons-atomic-theory.html Advancements John Dalton was the first to propose the idea of an atomic theory (see above.. all advancements). This was revolutionary and led to many other theories - becoming more advanced and precise each time. Limitations Since Dalton's theory was the first to propose the concept of an atom, his interpretation of an atom was extremely simple. His atom was a hard sphere that did not include any sub-atomic particles: protons, neutrons or electrons. Instead, he claimed that the atom is indivisible. With the discovery of these sub-atomic particles, it could no longer be argued that an atom is indivisible. The discovery of isotopes proved that the atoms of the same element are not always 100% identical. In Millikan's Oil Drop Experiment, he used an atomizer to spray tiny oil droplets and had them fall through a small, charged hole into a closed space containing two parallel metal plates. Due to the friction of the spraying, some of the oil droplets now had a small electric charge on them. When he connected a high-voltage battery to the plates, he observed the charged oil particles move up and down in the electric field. By analyzing the motion and calculating the speed of the particles, he was able to discover the charge on the drop and his observations led him to determine the elementary charge of a single electron: 1.6E-19 Coulombs. He noticed that all other values of charge were multiples of this value. Millikan made several significant discoveries regarding the electron:
1) He determined the charge on an electron and showed that charge is not a continuous quantity.
2) Since Thomson had discovered the electron and created a charge-to-mass ratio, Millikan was able to calculate a fairly accurate value for the mass of the electron. This showed that the mass of an electron is about 1700 times less than the mass of a hydrogen atom (which is the lightest atom) so this confirmed Thomson's prediction. Advancements Limitations ~Mathematics~
Determination of the Charge- to-Mass Ratio of an Electron ~Mathematics~
Determination of Elementary Charge Rutherford discovered the nucleus of an atom, which lead to the planetary model (or nuclear model) of the atom.
In Rutherford's model, the
electrons orbit the nucleus
similar to the planets orbiting the sun. The electrostatic attraction (between the +nucleus and -electons provided a centripetal force which keeps the electrons in orbit. Advancements Rutherford discovered the nucleus of the atom and that the electrons are not embedded. Due to his scattering experiments, he was able to determine that most of an atom's mass comes from the nucleus, which is formed of protons and neutrons. He calculated the size of the nucleus by applying the law of conservation of energy. He used the formula: Formulas: For an undeflected electron:
v=lEl/B For a deflected electron:
q/m=v/Br - - - - + + + + e- Cathode ray x x x x x x x B lEl (1) (2) (1) When the electric force is equal to the magnetic force, the electrons pass through the potential difference undeflected. The formula Fe=Fm can be broken down to the formula lElq=qvB. By rearranging this formula, we can solve for the velocity of an electron: v=lEl/B Potential difference (2) Once the velocity has been calculated, we can remove the electric field. This causes the path of the cathode ray to deflect. Then, we calculate the radius of the curvature (of e- path) by using the formula Fm=Fc. This formula breaks down to qvB=mv^2/r which Thomson rearranged to determine the charge-to-mass ratio: q/m=v/Br Example:
An ion travels in an arc of a measured radius of 0.037 m while moving at 1.5E5 (150,000) m/s perpendicular to a 0.50-T magnetic field. What is the charge-to-mass ratio? Since the magnetic force acts as the centripetal force:
q/m=8.1E6 C/Kg
The charge-to-mass ratio for this ion is approximately 8.1E6 C/Kg. Determining the Mass of an Electron Once Millikan calculated the Elementary charge, it was very simple to determine the mass of an electron thanks to Thomson's charge-to-mass ratio formula. q/m=v/Br
m=qBr/v Atomic Spectra Limitations Excited gas Excited gas Emission Spectra Absorption Spectra Bohr's Energy Levels In Rutherford's model, the electrons would be accelerating and radiating energy, therefore they would eventually lose energy. Therefore, there was a huge problem with the stability of the atom. According to electromagnetic theory, if an electron ran out of energy, it would fall into the nucleus. As we know, the number of protons in the nucleus of an atom cannot change. The atomic number of each element is unique. Some frequencies of light are absorbed as they pass from a hot dense material through an excited gas. These wavelength form the dark lines against the continuous spectrum. A hot gas at low pressure will produce a pattern of bright lines called an emission spectrum. These lines on the spectrum represent the frequencies of EMR emitted by the element. Elements absorb the same frequencies that they emit. The bright lines of the emission spectrum will correspond with the dark lines of the absorption spectrum; this is useful to identify them (using a spectrometer). Continuous Spectra A hot, dense material (such as an incandescent lightbulb) produces a continuous spectrum without any dark or bright lines because it emits all wavelengths of EMR. The Bohr model helps to explain the emission and absorption spectra. An electron can jump to a higher level by gaining energy. This energy is gained by the absorption of a photon. Since energy and frequency are related by the formula E=hf, the atom can only absorb the frequencies which correspond with the differences between its energy levels. Absorption of EMR at these frequencies results in the dark bands of the absorption spectrum. This is the same with the emission of photons which produce bright lines in the emission spectrum. -13.6 eV -3.4 eV -1.5 eV -0.85 eV -0.38 eV -0.54 eV n=1 n=2 n=3 n=4 n=5 n=6 The First 6 Energy Levels for Hydrogen Absorbs a photon
(absorbs EMR) Emits a photon
(emits EMR) Has to absorb a photon with 1.9 eV of energy
(difference between energy levels 2 and 3) (1.9 eV) e- e- e- e- Basic principles of Bohr's model:
Electrons orbit only at certain distances from the nucleus (which are particular multiples of the radius of the smallest orbit). That being said, the orbits in an atom are quantized.
Both Ek and Ep of an electron in orbit depend upon the distance from the nucleus. Therefore, the energy of an atom is also quantized. Each orbit is a different energy level for the electron. The lowest amount of energy is found in the smallest orbit.
Electrons move up an energy level by absorbing EMR, or down a level by emitting EMR. The energy of the light absorbed or emitted must be equal to the difference between the 2 energy levels. If an electron does not jump levels, it is not radiating energy. The orbits are called stationary states because they do not change size or shape and the energy level is fixed. Advancements Limitations It does not explain why energy is quantized or why the electrons in orbit do not radiate energy.
The model is not completely accurate for atoms with 2+ electrons.
Bohr's model could not explain the Zeeman effect: why the magnetic field splits the spectral lines into multiple closely spaced lines.
It poorly predicts the spectra of larger atoms and is unable to predict the relative intensities of spectral lines.
It does not explain fine structure or hyperfine structure in spectral lines.
Since Bohr's model considers that electrons have both a known radius and orbit, it violates the Heisenberg Uncertainty Principle.
The value for the ground state orbital angular momentum has been proven incorrect. Bohr expanded upon Rutherford's planetary model. He proposed that the electron orbits are stationary orbits. This was in order to overcome the problem of stability of an electron in orbit around a nucleus. Bohr's model helps to explain the emission and absorption spectra and to calculate the emission/absorption of energy as the electron jumps energy levels. Millikan stated that he used ALL of his data to come to his conclusion that charge is quantized. In the 1970s, it was discovered that his notebooks contained 175 measurements, but he only reported 58 of them. He used only certain numbers so that his data would work nicely. When all of his measurements were used, his evidence is not quite as conclusive. No one knows whether Millikan is guilty of scientific fraud, or if he had some sort of intuitive insight that led him to choose only certain data to prove his point regarding the quantization of charge. Advancements Limitations The Quantum model does not predict the exact location of an orbiting electron, but rather the likelihood of an electron being at any given point. For this reason, it is vague and sometimes a difficult concept to accept. In fact, some physicists (ie. Einstein and Schrödinger) had difficulty accepting this theory. Even though it is complex - yet cannot predict a precise point - it is the most accurate model. The Quantum model is based on the quantum theory, which states that matter has wave-like properties. According to this theory, it is impossible to know both the momentum and precise location of an electron in an atom (Uncertainty principle). This model uses orbitals (or electron clouds) to show volumes of space where there is likely to be an electron. It is based on probability rather than certainty. The Quantum model uses the wave-like properties of matter, therefore it provides a natural explanation for the quantization of energy levels. Also, it shows that an electron wave will occupy all 3 dimensions of space (as opposed to a guitar string, which will only vibrate in 2D). The model is extremely mathematical and can be proven by many complex equations. The Quantum Mechanical Model is the most current and accepted model in this day. Where...
Ep: electric potential energy that a charge q1 gains from the field around charge q2
k: Coulomb's constant
q: the charges
d: distance between charges (radius of nucleus can not exceed this number) He derived this equation from Coulomb's Law. Alpha particle Scattering Experiment: Most Alpha particles are undeflected A few alpha particles are slightly deflected A few alpha particles bounce off of nucleus The Set Up The Observations The Results Expectation Result Rutherford's expectations were based on the raisin-bun model of the atom where positive and negative charges are distributed evenly. The results were much different than he expected. Rutherford directed a beam of alpha particles through a slit in a circular screen toward a thin gold foil. Once passing through the foil, the deflected particles would strike the fluorescent screen and produce a visible flash of light called scintillation. Ep=kq1q2/d + + + + + - - - - - o o Fe (9.81N)

Fg (9.81N) = oil droplets 1) Suspended 2) Accelerating downwards 3) Accelerating Upwards 1) Suspended Oil Droplets 2) Drops accelerating Downwards 3) Drops accelerating upwards Charged particle with a mass of 2.7E-16
Accelerating upwards at 3.5 m/s^2
Between 2 horizontal parallel plates 0.11 m apart
Potential difference of 4.2E2 V
What is charge? How many electrons lost or gained? lEl=V/d
lEl=3818 N/C 1) 2) q=m(g+a)/lEl
q= 9.4E-19 C Electric field strength of 1.0E5 N/C (down)
Mass of 8.2E-15 Kg
What is the charge? How many electrons lost or gained? Fg=Fe
q=-8.04E-19 net charge= -8.04E-19/-1.6E-19
= 5e-
or gained 5 electrons 1) 2) 3) Net charge= 9.4E-19/1.6E-19
= 6e-
or gained 6 electrons Mass of 3.0E-16
Accelerating 6.5 m/s^2
Electric field strength of 3.2E3 N/C
What is charge and number of electrons gained or lost? 1) q=m(g-a)/lEl
q=3.1E-19 C 2) Net charge= 3.1E-19/1.6E-19
= 2e-
or gained 2 electrons m=mass
B=magnetic field strength
v=velocity g-a g+a o Hot dense solid
White light White light ~Becca Epp~
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