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Nucleus

Course: PHYS 131, Spring 2011
School: Cuyamaca College
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Nucleus Ernest The Rutherfords proposal that the atom consisted of negatively charged electrons orbiting a positively charged nucleus triggered a great deal of curiosity about the structure of that nucleus. It is important to understand how small it really is. If a hydrogen atom were the size of San Diego, the nucleus at the center would be smaller than a baseball. The atom as we understand it consists almost...

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Nucleus Ernest The Rutherfords proposal that the atom consisted of negatively charged electrons orbiting a positively charged nucleus triggered a great deal of curiosity about the structure of that nucleus. It is important to understand how small it really is. If a hydrogen atom were the size of San Diego, the nucleus at the center would be smaller than a baseball. The atom as we understand it consists almost entirely of empty space. The phenomenon of radiation emitted from certain rare minerals had been studied long enough to conclude that it came chiefly in three particle-like forms named alpha ( ), beta ( ), and gamma ( ). Alpha particles were heavy, comparatively slow, and positively charged, judging by they way they deflected in a magnetic field. They could be blocked effectively by a sheet of paper. Beta particles were much faster and lighter, negatively charged, and required something denser, like wood or skin, to stop them. Gamma particles appeared to move at the speed of light. They were uncharged and could penetrate several inches of lead. Clearly, these particles were coming out of the nucleus, so the nucleus must be composed of them, except the beta particle turned out to be nothing more than a very fast-moving electron and the gamma particle was found to be a high-frequency photonjust another kind of light. Accelerating alpha particles and smashing them into atoms resulted in the discover of a new particle that had exactly the same charge as an electron, but it was positive instead of negative and had a mass roughly 2000 times greater. Stranger still, it seemed to be identical to the nucleus of the hydrogen atom with the electron stripped off. It was called the proton. Another particle was found later having a nearly identical mass as the proton, but a neutral charge. It was named the neutron. The alpha particle was determined to consist of a bundle of two protons with two neutrons, and was identical to the nucleus of a helium atom. It was subsequently determined that all atoms are built out of these two nucleons, and so the persistent picture of a conglomeration of spherical nucleons at the center of the atom was born. The number of protons determines the number of electrons through electrostatic attraction. Since the electrons determine the chemical nature of the atom, the number of protons was labeled the atomic number and inexplicably given the symbol Z. Since neutrons have essentially the same mass as protons, and since electrons are vastly lighter than either, the mass of the atom is determined by the sum of the nucleons. This is called the mass number and given the symbol A. The approximate radius of the nucleus in femtometers (10 -15 m) can be found using r = 1.2 A1/3. Different numbers of neutrons do not affect the chemical identity of the element. These different varieties of the same element are called isotopes. For the one-hundred-plus elements found so far, more than a thousand isotopes are known. The vast majority of these are unstable (radioactive), so there is clearly a magic relationship between the number of protons and neutrons to make an isotope stable. Above element 82 (lead), all known isotopes are radioactive. Additionally, elements 43 and 61 (technetium and promethium) do not have stable forms. As a rough approximation, you can estimate the atomic weight (mass) of an element from its atomic number using Z(2+Z/150) and rounding downward to the preceding integer.
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Cuyamaca College - PHYS - 131
Physics 131 Practice Test 1fieldpoint1. Find the electric field vector at the point shown.Use k = 910.3my4mx-125nC2. What is the electric field 10cm from the central axis of a long, uniform metal bar uponwhich a total charge of 120C has been pl
Cuyamaca College - PHYS - 131
The Photoelectric EffectThe exploration of interference phenomena had indicated that light existed as wavesincontrast to gases, for example, which were clearly composed of discrete particles. Rightat the start of the twentieth century, however, experim
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Practice Exam 21. Light with a wavelength of 600nm passes through the double-slitshown. If the distance to on the projection screen from the center to thefirst-order maximum is 0.1m, how far is the screen from the double-slit?60000nm-50mC2. Find the
Cuyamaca College - PHYS - 131
Practice Test 1 Answers1. (-36x -27y )N/C2. 0 (Charge all migrates to the surface of metal.)3. (9/0)r N/C4. 5mN5. 4F6. 50mW7. A,D,B,C or A,D,C,B8. 4e -t/0.6s V9. 290 A10. (-500y -1000z )q0 N
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Quantum NumbersSo far, we are aware of three integer quantum numbers for atoms: the principal (n > 0),the angular (0 l < n), and the magnetic (-l m l ). It was subsequently shown thatthere must be a fourth quantum number bearing a separate resonance of
Cuyamaca College - PHYS - 131
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Cuyamaca College - PHYS - 131
(Quiz 01 was simply attendance on the first day.)First find |E|=kQ/r. This requires finding r = (x + y) = (8 + 6) = 100 = 10.So |E| = -kQ/100. (Note that Q has been replaced with -Q as specified.Next, Ex = |E|(x/r) = (-kQ/100)(-8/10) = +8kQ/1000 = kQ/1
Cuyamaca College - PHYS - 131
RC CircuitsA circuit consisting of one resistor and one capacitor can exhibit exponential behaviordue to the time it takes to charge the capacitor and to the resistors prevention ofunlimited current flow. The curves shown below are intended to remind y
Cuyamaca College - PHYS - 131
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Cuyamaca College - PHYS - 131
Refraction EffectsSuppose, for ease of calculation, that we have a sample of a material with an index ofrefraction of exactly 2, and we are observing the effects of shining a laser out of thematerial to the surrounding air (n = 1) at various angles. As
Cuyamaca College - PHYS - 131
Relativistic VelocityAt the core of physics, at least in principle, is the notion of logical consistency: A factisnt a fact if it contradicts itself. If we can overcome our natural human resistance toaccepting counterintuitive realities, there is a gre
Cuyamaca College - PHYS - 131
Special RelativityWe have seen that relativity requires a correction to the speed of an object as measuredfrom a different inertial framespecifically, this denominator: 1 vv/c. Notice,however, that for small values of v or v, this corrective factor is
Cuyamaca College - PHYS - 131
Resistive DC CircuitsDirect current (DC) means that the current flow in a circuit is steadyrather than varying in time. Batteries and plug-in chargers for variousdevices are two examples of DC. The usual symbol for a battery isshown at right, along wi
Cuyamaca College - PHYS - 131
ResistorsA resistor is an electrical circuit element made out of a material that conducts electricalcurrent, but not as well as a metal wire. Electrical current (I) is the flow of electricalcharges, and in direct current (DC) circuits, is pictured as g
Cuyamaca College - PHYS - 131
The Rydberg EquationUsing the quantum mechanical resonance model for the electron cloud in atoms, we canunderstand the absorption or emission of photons as resulting from the electron cloudexpanding out to a larger shell or contracting inward to a smal
Cuyamaca College - PHYS - 131
Simplifying Resistive and Capacitive NetworksAny network made purely of resistors or of capacitors can theoretically be simplifieddown to a single equivalent value by replacing each valid series or parallel pair with theappropriate equivalent. It is as
Cuyamaca College - PHYS - 131
Single-Aperture InterferenceWhen coherent light shines through a single small slit onto a screen, the multiple slitdiffraction equation (2l s i n = N ) fails to predict the maxima and minima. The firstproblem is that l was used to describe the distance
Cuyamaca College - PHYS - 131
Thin-Film InterferenceWhen any wave encounters an interface between mediums, there is always a reflectionbackward from the interface whether or not part of the wave continues into the newmedium. Consider a thin film of oil on the surface of a puddle of
Cuyamaca College - PHYS - 131
Thin LensesA lens wouldnt be much good if theonly function it had was to focus orspread parallel rays coming from anear-infinite distance. Fortunately,lenses perform interesting operationson rays under other conditions, too.For instance, a convergi
Cuyamaca College - PHYS - 131
Radiation ToxicityThe image at right depicts a molecule of an extremely toxic substance. Since itsinitial identification in 1917, it has been shown that a dose as little as 10 mg canresult in painful softening and swelling of the bones, yellowing and p
Cuyamaca College - PHYS - 131
TransformersA transformer is an electrical devicethat takes advantage of inductance inorder to convert one voltage/current toanother voltage/current. The basicIconstruction is shown in the figure toIthe right. Two coils of wire are wound+around
Cuyamaca College - PHYS - 131
The Uncertainty PrincipleIf the entire universe consists of waves when viewed on the smallest scales, what is aparticle? A particle is a wave packet. Consider the graph shown below where two sinewaves of slightly different frequency are superposed, cre
Cuyamaca College - PHYS - 131
Using RelativityHaving been shown the odd equations that must beemployed when relativistic speeds are involved, itis now time for you to see how to use them. Oneuseful device for glimpsing the peculiarities ofrelativity is a modified form of a space-
Cuyamaca College - PHYS - 131
Voltage (Electric Potential)If the path by which charged particles follow an electric field does not matter, such as forelectrons in an electrical circuit, it would be more convenient to have a non-vectorquantity that essentially indicates how much pot
Cuyamaca College - PHYS - 131
WaviclesIt has previously been shown to follow directly from Maxwells equations that for anelectromagnetic wave of constant average intensity, the photonic pressure P in emptyspace is given by P = P/Ac, where P is the power in the wave, A is the area,
Cuyamaca College - PHYS - 131
X-Ray SpectraWe have seen that hydrogen emission lines come in groups, and that the shortestwavelengths of light it can produce fall in the UV portion of the spectrum. Clearly, x-raywavelengths would have to come from other atoms. In fact, the Rydberg
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