Quantum Numbers and Rules

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Band 7In some countries children have very strict rules of behaviour, in other countries they are allowed to do almost anything they want. To what extent should children have to follow rules? Freedom plays a mandatory role in everybody?s life. We can see in today?s modernized era nobody likes to get some restrictions upon them, whether it would be a child or an adult. Some people think that there should have some strict rules of behaviour for children, but I disagree with this statement. Wherever it is a reality that sometimes more restrictions can cause more frustration in children, which leads to many other mental diseases as well. Morever they can be, behave like a stubborn. Sometimes they feel themselves under pressure, which can be a main reason for their poor performance in their field. In some cases children would be crazier to do these things from where we?ll try to keep them away. In other words _ we have to look for other aspects as well, like if we usually ignore our children?s bad habits, then they can?t be good human beings in their future life. Moreover_ if we never draw attention upon the children?s main activities then they may be acquiring bad company. They can know regarding the value of respect for their elders. They can know the importance of relationships. They can know regarding their cultural values as well. In a nutshell, I would like to say that children should be teach regarding the value of their customs, rituals and respect towards their elders for their future life, but most of the extra restriction should be being avoided. It would be better to make them good human beings in their coming future. Quantum Numbers and Rules Quantum Numbers and Rules Bởi: OpenStaxCollege Physical characteristics that are quantized—such as energy, charge, and angular momentum—are of such importance that names and symbols are given to them The values of quantized entities are expressed in terms of quantum numbers, and the rules governing them are of the utmost importance in determining what nature is and does This section covers some of the more important quantum numbers and rules—all of which apply in chemistry, material science, and far beyond the realm of atomic physics, where they were first discovered Once again, we see how physics makes discoveries which enable other fields to grow The energy states of bound systems are quantized, because the particle wavelength can fit into the bounds of the system in only certain ways This was elaborated for the hydrogen atom, for which the allowed energies are expressed as En ∝ 1/n2, where n = 1, 2, 3, We define n to be the principal quantum number that labels the basic states of a system The lowest-energy state has n = 1, the first excited state has n = 2, and so on Thus the allowed values for the principal quantum number are n = 1, 2, 3, This is more than just a numbering scheme, since the energy of the system, such as the hydrogen atom, can be expressed as some function of n, as can other characteristics (such as the orbital radii of the hydrogen atom) The fact that the magnitude of angular momentum is quantized was first recognized by Bohr in relation to the hydrogen atom; it is now known to be true in general With the development of quantum mechanics, it was found that the magnitude of angular momentum L can have only the values h L = √l(l + 1) 2π (l = 0, 1, 2, , n − 1), 1/10 Quantum Numbers and Rules where l is defined to be the angular momentum quantum number The rule for l in atoms is given in the parentheses Given n, the value of l can be any integer from zero up to n − For example, if n = 4, then l can be 0, 1, 2, or Note that for n = 1, l can only be zero This means that the ground-state angular momentum for hydrogen is actually zero, not h / 2π as Bohr proposed The picture of circular orbits is not valid, because there would be angular momentum for any circular orbit A more valid picture is the cloud of probability shown for the ground state of hydrogen in [link] The electron actually spends time in and near the nucleus The reason the electron does not remain in the nucleus is related to Heisenberg’s uncertainty principle—the electron’s energy would have to be much too large to be confined to the small space of the nucleus Now the first excited state of hydrogen has n = 2, so that l h can be either or 1, according to the rule in L = √l(l + 1) 2π Similarly, for n = 3, l can be 0, 1, or It is often most convenient to state the value of l, a simple integer, rather h than calculating the value of L from L = √l(l + 1) 2π For example, for l = 2, we see that h h L = √2(2 + 1) 2π = √6 2π = 0.390h = 2.58 × 10 −34 J ⋅ s It is much simpler to state l = As recognized in the Zeeman effect, the direction of angular momentum is quantized We now know this is true in all circumstances It is found that the component of angular momentum along one direction in space, usually called the z-axis, can have only certain values of Lz The direction in space must be related to something physical, such as the direction of the magnetic field at that location This is an aspect of relativity Direction has no meaning if there is nothing that varies with direction, as does magnetic force The allowed values of Lz are h Lz = ml 2π (ml = − l, − l + 1, , − 1, 0, 1, l − 1, l), where Lz is the z-component of the angular momentum and ml is the angular momentum projection quantum number The rule in parentheses for the values of ml is that it can range from − l to l in steps of one For example, if l = 2, then ml can have the five values –2, –1, 0, 1, and Each ml corresponds to a different energy in the presence of a magnetic field, so that they are related to the splitting of spectral lines into discrete parts, as discussed in the preceding section If the z-component of angular momentum can have only certain values, then the angular momentum can have only certain directions, as illustrated in [link] 2/10 Quantum Numbers and Rules The component of a given angular momentum along the z-axis (defined by the direction of a magnetic field) can have only certain values; these are shown here for l = 1, for which ml = − 1, 0, and +1 The direction of L is quantized in the sense that it can have only certain angles relative to the z-axis What Are the Allowed Directions? Calculate the angles that the angular momentum vector L can make with the z-axis for l = 1, as illustrated in [link] Strategy [link] represents the vectors L and Lz as usual, with arrows proportional to their magnitudes and pointing in the correct directions L and Lz form a right triangle, with L being the hypotenuse and Lz the adjacent side This ... No. 2007-06-A O FFICE OF E CONOMICS W ORKING P APER U.S. I NTERNATIONAL T RADE C OMMISSION Alan K. Fox U.S. International Trade Commission William Powers U.S. International Trade Commission Ashley Winston Centre of Policy Studies, Monash University, and U.S. International Trade Commission June 2007 The authors are with the Office of Economics of the U.S. International Trade Commission. Office of Economics working papers are the result of the ongoing professional research of USITC Staff and are solely meant to represent the opinions and professional research of individual authors. These papers are not meant to represent in any way the views of the U.S. International Trade Commission or any of its individual Commissioners. Working papers are circulated to promote the active exchange of ideas between USITC Staff and recognized experts outside the USITC, and to promote professional development of Office staff by encouraging outside professional critique of staff research. Address correspondence to: Office of Economics U.S. International Trade Commission Washington, DC 20436 USA Textile and Apparel Barriers and Rules of Origin in a Post-ATC World Textile and Apparel Barriers and Rules of Origin in a Post-ATC World Alan Fox U.S. International Trade Commission, Washington, DC William Powers U.S. International Trade Commission, Washington, DC Ashley Winston Centre of Policy Studies, Monash University, and U.S. International Trade Commission June 2007 Abstract Although textile and apparel imports from most countries entered the United States quota-free after the expiration of the Agreement on Textiles and Clothing on January 1, 2005, substantial restraints remain on U.S. trade in these sectors. These restraints include high tariffs, quantitative restraints on some large exporters, and rules of origin that apply to duty-free imports from preferential trading partners. While there is a substantial literature on quotas and tariffs in these sectors, this paper provides a new and detailed examination of preferential rules of origin, including both compliance costs and rule-based foreign demand for U.S. textile and apparel inputs. This paper uses the USAGE–ITC model to estimate U.S. welfare gains and sectoral effects of removing all textile and apparel restraints in 2005. Liberalization is estimated to increase U.S. welfare by $3.5 billion (net) while decreasing U.S. textile and apparel output by $11.0 billion. Eliminating only quantitative restraints provides over half of the welfare gain but causes less than 2 percent of the output loss, with a large decline in only the sock sector. Tariff elimination provides about one quarter of the welfare gain at a cost of 13.3 percent of the output loss, while elimination of preferential rules of origin accounts for the remaining 23.3 percent of increased welfare and 84.9 percent of the overall output reduction. These results highlight the important effects of  Real Numbers All numbers on the SAT are real numbers. Real numbers include the following sets: ■ Whole numbers are also known as counting numbers. 0,1,2,3,4,5,6, . ■ Integers are positive and negative whole numbers and the number zero. . . . –3, –2, –1, 0, 1, 2, 3 . . . ■ Rational numbers are all numbers that can be written as fractions, terminating decimals, and repeating decimals. Rational numbers include integers. ᎏ 3 4 ᎏᎏ 2 1 ᎏ 0.25 0.38658 0.6 ෆ 6 ෆ 6 ෆ ■ Irrational numbers are numbers that cannot be expressed as terminating or repeating decimals. π ͙2 ෆ 1.6066951524 . . . CHAPTER Numbers and Operations Review This chapter reviews key concepts of numbers and operations that you need to know for the SAT. Throughout the chapter are sample ques- tions in the style of SAT questions. Each sample SAT question is fol- lowed by an explanation of the correct answer. 5 37 Practice Question The number –16 belongs in which of the following sets of numbers? a. rational numbers only b. whole numbers and integers c. whole numbers, integers, and rational numbers d. integers and rational numbers e. integers only Answer d. –16 is an integer because it is a negative whole number. It is also a rational number because it can be written as a fraction. All integers are also rational numbers. It is not a whole number because negative numbers are not whole numbers.  Comparison Symbols The following table shows the various comparison symbols used on the SAT. SYMBOL MEANING EXAMPLE = is equal to 3 = 3 ≠ is not equal to 7 ≠ 6 > is greater than 5 > 4 ≥ is greater than or equal to x ≥ 2 (x can be 2 or any number greater than 2) < is less than 1 < 2 ≤ is less than or equal to x ≤ 8 (x can be 8 or any number less than 8) Practice Question If a > 37, which of the following is a possible value of a? a. –43 b. –37 c. 35 d. 37 e. 41 Answer e. a > 37 means that a is greater than 37. Only 41 is greater than 37. – NUMBERS AND OPERATIONS REVIEW – 38 Symbols of Multiplication A factor is a number that is multiplied. A product is the result of multiplication. 7 ϫ 8 ϭ 56. 7 and 8 are factors. 56 is the product. You can represent multiplication in the following ways: ■ A multiplication sign or a dot between factors indicates multiplication: 7 ϫ 8 ϭ 56 7 • 8 ϭ 56 ■ Parentheses around a factor indicate multiplication: (7)8 ϭ 56 7(8) ϭ 56 (7)(8) ϭ 56 ■ Multiplication is also indicated when a number is placed next to a variable: 7a ϭ 7 ϫ a Practice Question If n ϭ (8 – 5), what is the value of 6n? a. 2 b. 3 c. 6 d. 9 e. 18 Answer e. 6n means 6 ϫ n, so 6n ϭ 6 ϫ (8 Ϫ 5) ϭ 6 ϫ 3 ϭ 18. Like Terms A variable is a letter that represents an unknown number. Variables are used in equations, formulas, and math- ematical rules. A number placed next to a variable is the coefficient of the variable: 9d 9 is the coefficient to the variable d. 12xy 12 is the coefficient to both variables, x and y. If two or more terms contain exactly the same variables, they are considered like terms: Ϫ4x,7x, 24x, and 156x are all like terms. Ϫ8ab,10ab, 45ab, and 217ab are all like terms. Variables with different exponents are not like terms. For example, 5x 3 y and 2xy 3 are not like terms. In the first term, the x is cubed, and in the second term, it is the y that is cubed. – NUMBERS AND OPERATIONS REVIEW – 39 You can combine like terms by grouping like terms together using mathematical operations: 3x ϩ 9x ϭ 12x 17a Ϫ 6a ϭ 11a Practice Question 4x 2 y ϩ 5y ϩ 7xy ϩ 8x ϩ 9xy ϩ 6y ϩ 3xy 2 Which of the following is equal to the expression above? a. 4x 2 y ϩ 3xy 2 ϩ 16xy ϩ 8x ϩ 11y b. 7x 2 y ϩ 16xy ϩ 8x ϩ 11y c. 7x 2 y 2 ϩ 16xy ϩ 8x ϩ 11y d. 4x 2 y ϩ 3xy 2 ϩ 35xy e. 23x 4 y 4 ϩ 8x ϩ 11y 1 - 5 CCNA 2: Routers and Routing Basics v 3.0 - Lab 10.2.5 Copyright  2003, Cisco Systems, Inc. Lab 10.2.5 Well-Known Port Numbers and Multiple Sessions Objective • Enable HTTP services on a router. • Show multiple HTTP and Telnet sessions on a single host. • Observe well-known TCP port numbers on the host and router. Background/Preparation Cable a network similar to one of the diagram. Any router that meets the interface requirements displayed on the above diagram, such as 800, 1600, 1700, 2500, 2600 routers, or a combination, may be used. Please refer to the chart at the end of the lab to correctly identify the interface identifiers to be used based on the equipment in the lab. The configuration output used in this lab is produced from 1721 series routers. Any other router used may produce a slightly different output. The following steps are intended to be executed on each router unless specifically instructed otherwise. Start a HyperTerminal session as performed in the Establishing a HyperTerminal session lab. Note: Go to the erase and reload instructions at the end of this lab. Perform those steps on all routers in this lab assignment before continuing. 2 - 5 CCNA 2: Routers and Routing Basics v 3.0 - Lab 10.2.5 Copyright  2003, Cisco Systems, Inc. Step 1 Configure the hostname, passwords and interface on the Gadsden router a. On the Gadsden router, enter the global configuration mode and configure the hostname as shown in the chart. Then configure the console, virtual terminal, and enable passwords. Configure the Ethernet interface. Step 2 Save the configuration information from the privileged EXEC command mode GAD#copy running-config startup-config Step 3 Configure the host with the proper IP address, subnet mask and default gateway Step 4 Allow HTTP access to the router a. Allow HTTP access by issuing the ip http server command in global configuration mode. Step 5 Use the workstation browser to access the router a. Open a browser on Host 1 and type http://ip-address of Router GAD. There will be a prompt for the enable password of the router. Step 6 Telnet to the Ethernet interface on the router from the host Step 7 Start a second Telnet session to router Step 8 Start a third Telnet session to router by opening another command prompt Step 9 Start a fourth Telnet session to router by opening another command prompt Step 10 Check the number of sessions on the host a. Open another command prompt on the host and type netstat /? at the DOS prompt. b. What options are available for the netstat command? __________________________________________________________________________ c. Now type netstat –n. d. How many open sessions are there? ___________________________________________ e. What are the open sessions? _________________________________________________ f. What are the port numbers? __________________________________________________ Step 11 Check the number of sessions on the Router a. At the privileged EXEC mode type show tcp. b. How many open sessions are there? ___________________________________________ c. What are the open sessions? _________________________________________________ d. What are the port numbers on the sessions? ______________________________________ e. Why can all the sessions use port 23 (under Foreign Address)? __________________________________________________________________________ 3 - 5 CCNA 2: Routers and Routing Basics v 3.0 - Lab 10.2.5 Copyright  2003, Cisco Systems, Inc. f. List some of the Local Address port numbers (number after the colon following the IP address). __________________________________________________________________________ g. Why are all of the Local Address ... particles and integral spin particles Protons and neutrons, like electrons, have s = / 2, whereas photons have s = 1, and other particles called pions have s = 0, and so on 5/10 Quantum Numbers and Rules. .. 6/10 Quantum Numbers and Rules Probability clouds for the electron in the ground state and several excited states of hydrogen The nature of these states is determined by their sets of quantum numbers, ... ( ) Conceptual Questions Define the quantum numbers n, l, ml, s, and ms For a given value of n, what are the allowed values of l? 8/10 Quantum Numbers and Rules For a given value of l, what are