Directed Numbers - Addition & Subtraction

Understanding Quantum Theory of Electrons in Atoms The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 9.4.1). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom: The values nf and ni are the final and initial energy states of the electron. The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital. Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1. Consider the examples in Figure 9.4.2. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found. Principal quantum number (n) & Orbital angular momentum (l): The Orbital Subshell: https://youtu.be/ms7WR149fAY If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 9.4.3. Figure 9.4.4 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number ms=12. The other is called the β state, with the z component of the spin being negative and ms=−12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having ms=−12 and ms=12 are different if an external magnetic field is applied. Figure 9.4.5 illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 12 spin quantum number and down (in the negative z direction) for the spin quantum number of −12. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with ms=12 has a slightly lower energy in an external field in the positive z direction, and an electron with ms=−12 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting. The Pauli Exclusion Principle An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly

DIRECTED NUMBERS

F1 Class Quiz 3: Directed numbers

Practice adding and subtracting directed numbers

F1 Class Quiz 2: Fractions and Directed Numbers

How is personal data collected? There are several ways that an unauthorised person can try and collect your data. These include: •phishing •smishing •vishing •pharming. Phishing Phishing is when a person sends a legitimate looking email to a user. The email contains a link to a website that also looks legitimate. The user is encouraged to click the link and to input personal data into a form on the website. The email could also simply ask the user to reply to the email with their personal data. The user is tricked into giving their personal data to a source that they believe is legitimate. However, both the email and the linked website are from a fake unauthorised source. The personal data that is input is then collected by an unauthorised person. This person can then use this data for criminal acts, for example, to commit fraud or steal the person's identity. Intimidation has become a common feature of phishing emails, threatening the user that they must click the link and rectify a situation immediately, or there will be a further issue. The aim of a phishing attack is to steal the user's personal data. Figure 5.1: Phishing. A real-life example of phishing PayPal have been the subject of several different phishing emails. Users receive an email that looks as though it has been sent from PayPal, as it has the PayPal branding. The email normally warns of an issue such as unexpected activity on their account, or that some kind of verification of their account is required. The user is then asked to click a link to log into their account and resolve the issue. The link takes them to a webpage that looks like the PayPal login page. If the user inputs their login details into this page, they will not be taken to their account. It is often at this stage that the user may realise that the email and webpage are fake. However, they have already given the unauthorised person their PayPal login details. Figure 5.2: An example of a phishing email claiming to be from PayPal. How to recognise phishing There are several guidelines to be aware of regarding emails to avoid being subjected to phishing. These include: •Don't even open an email that is not from a sender that you recognise or a trusted source. •Legitimate companies will never ask you for your personal data using email. Be immediately suspicious of any email that requests your personal data. •Legitimate companies will normally address you by your name. Be suspicious of any email that addresses you as ‘Dear Member' or ‘Dear Customer'. •Legitimate companies will send an email that uses their domain name. If you hover your mouse over the sender's name, it will show the email address that the email is sent from. If this does not look legitimate, for example, does not contain the correct domain name, then it is probably fake. For example, if the sender's email is user@paypal1.com rather than user@paypal.com, this is from an incorrect domain name. •Legitimate companies are protective of their professional reputation and thoroughly check any communications. They will make sure that all information given is grammatically and correctly spelt. Be suspicious of any email that contains bad grammar or spelling mistakes. •A link in an email from a legitimate company will also normally contain the domain name of the company. You can sometimes hover over the link, or right click and inspect the link, to see the address of the URL that is attached. If the URL does not contain the domain name, or also contains typical errors such as spelling mistakes, then be suspicious of this. PRACTICAL ACTIVITY 5.02 Ask a friend or a member of your family if they have ever received an email that they believed was a phishing email. Ask them how they identified it was phishing. Ask them if they know all of the given guidelines for identifying phishing emails. Smishing Smishing (or SMS phishing) is a variant of phishing that uses SMS text messages to lure the user into providing their personal details. The user is sent an SMS text message that either contains a link to a website, in the same way that phishing does, or it will ask the user to call a telephone number to resolve an urgent issue. The same advice can be followed for smishing as given for phishing. The user must question at all times any links that are sent from an unknown or suspicious user. It is advisable that if a user believes the message may be legitimate, to type in the domain name for the legitimate company website into their web browser, rather than following the link in the message. Users should block any numbers that they believe are suspicious to prevent any further risk of smishing from that number. Figure 5.3: Smishing. Vishing Vishing (or voice phishing) has the same aim as phishing, to obtain a user's personal details. The user receives a telephone call that could either be an automated system or could be a real person. An automated voice could speak to the user and advise them that an issue has occurred, such as there has been suspicious activity regarding their bank account. The user may then be asked to call another number, or just to simply press a digit and be directed to another automated system. This system will ask them to provide their bank account details to resolve the issue. The bank account details have then been obtained by the unauthorised user and can be used to commit a crime against the user. The automated system could be replaced by a real person who will try to do the same thing. They will try to convince the user that there has been an issue with an account they have and to provide the log-in details or PIN for the account to verify who they are so the issue can be resolved. The precaution to take for vishing is that no company will ever call you and ask you to provide any log-in details or PIN details over the telephone. They may ask you to provide other personal information, and if you are in doubt that the person on the other end of the phone is legitimate, it is always advisable to put the phone down and call the company back on a legitimate number that you may already know or can obtain. Figure 5.4: Vishing. Pharming Pharming is when an unauthorised user installs malicious code on a person's hard drive or server. The malicious code is designed to redirect a user to a fake website when they type in the address of a legitimate one. The fake website is designed to look like the legitimate one, to trick the user and make sure they are not aware that their request has been redirected. The user will then enter their personal details into the fake website, believing it is the legitimate one, and the unauthorised person will now have their personal data. A common technique used in pharming is called domain name server (DNS) cache poisoning. This technique exploits vulnerabilities in the DNS and diverts the internet traffic intended for a legitimate server toward a fake one instead. The unauthorised user needs to find a way to install the malicious code on the computer. They often hide the malicious code in an email attachment or link. When the user opens the email attachment or clicks the link, the malicious code is downloaded also. Figure 5.5: Pharming. The aim of a pharming attack is also to steal a user's personal data. A real-life example of pharming In 2007 50 different companies all over the world were subject to a pharming attack, these included PayPal, eBay, Barclays bank and American Express. Over a three-day period, hackers managed to infect over 1000 PCs a day with a malicious pharming code. When users who had been infected visited the websites of the different companies, they were redirected to a legitimate-looking version of the site that was designed to steal their personal data. The original email, containing the malicious code, was set up to look like a shocking news story. Users were encouraged to click a link in the email to find out more information. The code was downloaded when the user clicked the link. This was quite a sophisticated attack that required legitimate looking websites to be set up for a large number of companies. It is not known how much money the hackers were able to retrieve as a result. How to prevent pharming All of the guidelines to avoid being subjected to phishing are also relevant for recognising pharming. There are also several other precautions that can be taken to check for pharming attacks. These include: •Have a firewall installed and operational. A firewall monitors incoming and outgoing traffic from your computer. It checks this traffic against set criteria and will flag and stop any traffic that does not meet the criteria. A firewall could detect and block suspicious traffic, such as a malicious code trying to enter your system. •Have an anti-virus program installed that is designed to detect malicious pharming code. You need to scan your computer on a regular basis to check for any malicious code. It is advisable to set up an automatic scan on a daily basis at a time when your computer will normally be switched on. •Be aware when using public Wi-Fi connections. A hacker could look to directly access your computer and install the malicious code if you are connected to a public Wi-Fi connection. It is often advisable to use a VPN when using public Wi-Fi. This will help shield your internet activity and personal details from a hacker, making it more difficult for them to access your computer. Smishing can also be used as a form of pharming. A user is sent a link, that when they click is designed to download malware onto their mobile device. Therefore, it is advisable to have security software installed on your mobile and also scan it regularly to detect any presence of malware.

1.1945-1949: The immediate years after the Second World War ● At the end of 1945, Mao Zedong had come to see the USA as the greatest threat to his aspirations. a. He understood that East Asians were looking to the USA as the true liberator from Japanese imperialism. b. The USA’s support for the Kuomintang(KMT) and the restoration of U.S. authority in formerly Japanese Manchuria clashed with the CCP’s plans to use the region for its own needs in the impending civil war between the CCP and the GMD. ■ To compound matters, while the KMT was recognised internationally as the official government in China, Mao and the CCP saw the party as a puppet of U.S. imperialism. ● While Mao saw the USA as the greater threat to the CCP’s plans, Soviet actions also frustrated him. a. The USSR provided minimal and incoherent support for the Chinese Communists in Yan’an and Manchuria. b. Stalin also attempted to extract territorial and economic concessions from the Guomindang government in the Friendship and Alliance Treaty China signed in August 1945 under American and Soviet pressure in exchange for Soviet entry into the Second World War against Japan. ● The emerging superpower conflict over Europe and over American intervention in the impending civil war in China led to Mao’s ideological perception of the 8838/01 H1 History Paper 1 Theme II: The Cold War and East Asia (1945-1991) \ Page | 8 USA as an aggressive imperialist power that was hostile towards other countries, especially the USSR and China. ● In 1946, Mao promoted the theory of the intermediate zone, which envisioned a global united front against American imperialism. a. Mao saw the emerging superpower conflict as an American-Soviet contest for the intermediate zones, the capitalist, colonial and semi- colonial countries of West Europe, Africa, and Asia. b. Mao believed that the USSR was the defender of world peace. c. The intermediate zone, which included China, would not be part of the socialist camp. d. Despite the tremendous potential that U.S. aid held for China’s reconstruction, Mao’s ideological worldview and the impending civil war against the Guomindang prevented him from seeking normalised relations with the USA. In 1949, Mao decided to lean towards the side of the USSR despite two decades of unreliable support from them. e. Mao saw the anti-bourgeois campaigns in East Europe as evidence that China should isolate capitalist-bourgeois forces within it.2 f. Stalin had expelled Yugoslavia from the socialist camp as its leader, Tito was seen to have directly challenged Stalin’s authority. ■ Mao thus saw it as imperative to stress close unity to the USSR lest he was seen as a second Josip Broz Tito. At the same time, Mao sought a loose partnership with the USSR because Mao believed that China should preserve a high measure of self- reliance and zili gengsheng (自力更生) (regeneration through one’s own efforts). ● When the People’s Republic of China was formed on 1 October, 1949, relations between China’s and the USSR’s communists had improved substantially. a. However, the Chinese Communist Party (CCP) was also aware that the USSR never treated Chinese interests as a priority. What the CCP failed to fully understand was that Stalin ruled East Europe much like it was his empire and how this would have implications for China. b. In Mao’s first visit to the USSR in December 1949, Stalin was non- committal regarding the interests raised by the Chinese, and treated Mao as an underling as he feared that closer relations with the PRC would cause the USSR to lose privileges gained from the KMT. _________________________ 2 What Mao did not realise at that point was that the anti-bourgeois campaigns in East European countries were part of Stalin’s intentional design to consolidate the power of communists in them. 8838/01 H1 History Paper 1 Theme II: The Cold War and East Asia (1945-1991) \ Page | 9 A note on Sino-American relations 2. Early 1950: The USA’s hands-off policy towards Taiwan begins to change ● By early 1950, the Truman administration had written off Taiwan and believed it was only a matter of time before the island fell to the PLA. ● Two events in early 1950 changed the USA’s position on East Asia. ○ The formation of the USSR-PRC alliance in February 1950 ○ The North Korean invasion of South Korea in June 1950 3. 1950: The Sino-Soviet Friendship, Alliance and Mutual Assistance Treaty ● Signed on 14 February, 1950. 3.1Implications for Sino-Soviet relations ● Stalin saw it as a means to get concessions that he had failed to get from the Kuomintang (KMT) government in 1945. ● For Mao and the newly founded People’s Republic of China (PRC), the alliance would provide security against U.S. imperialism and allow the PRC to get economic aid for reconstruction from the USSR. ● The Chinese realised soon after the 1950 treaty had been signed that the Soviet Union was intent on exploiting the agreement in its own favour. 8838/01 H1 History Paper 1 Theme II: The Cold War and East Asia (1945-1991) \ Page | 10 ● The Sino-Soviet alliance was officially directed against Japanese militarism and its allies, especially the USA. ● The Sino-Soviet alliance comprised three elements: party, military and economic relations. ○ Party: The Chinese Communist Party (CCP) was included in the customs of communist party internationalism, such as regular exchange of party delegations to congresses of the fraternal parties in Stalin’s socialist camp. ■ This move was meant to bring the PRC’s ideological beliefs about communism into greater alignment with the USSR’s. ○ Military: The alliance was supposed to provide the newly formed and weak PRC with a strategic deterrent and military aid against the USA on three fronts: Guomindang-held Taiwan, divided Korea, and Vietnam where France attempted to reestablish its colonial control. ■ Convinced that the USA would aggressively seek ways to undermine the CCP-led PRC through Taiwan, Korea and Vietnam, Mao sought an active defence. ● While in Moscow, Mao unsuccessfully asked Stalin to provide military assistance for the liberation of Taiwan. ● At the beginning of 1950, the PRC delivered large-scale military aid to Hanoi. The PRC was the first country to grant the communist-led Democratic Republic of Vietnam diplomatic recognition on 18 January 1950; Mao persuaded Stalin to do so on 30 January 1950. ● The PRC committed itself to North Korea, where Mao saw the commitment to North Korea both as a defence against U.S. imperialism and as support for a fellow communist country. ○ Economic: During Mao’s first stay in Moscow, Stalin had personally promised the delivery of fifty projects for primary industrialisation. ■ The agreement also led to a series of supplementary ones, such as a US$ 300 million loan that the PRC would repay with a mixture of strategic materials, rubber, agricultural products, goods for daily use and hard currency. ■ Significantly, Stalin used Soviet military and economic aid to extract concessions similar to those he failed to get from the Guomindang government in 1945. ■ The USSR and PRC would disagree on the pace and extent of the PRC’s planned development. ● In the last five weeks of Stalin’s life in early 1953, he attempted to pressure the PRC to reduce the planned 8838/01 H1 History Paper 1 Theme II: The Cold War and East Asia (1945-1991) \ Page | 11 development speed to a mere annual growth of 13-14 percent, and to plan individual projects in detail beforehand. These moves would potentially result in the PRC’s economy growing at a slower rate than initially projected. ● However, after Stalin’s death on 5 March 1953, the PRC’s Zhou Enlai decided to use his visit of condolence to the USSR to press forward negotiations. ○ When talks resumed in 1 April 1953, Beijing pressed for 150 Soviet industrial projects, but Moscow reduced them to 91 on the basis of insufficient data provided by the Chinese. ■ The economic disarray after China’s civil war and the economic pressures that came with the Korean War influenced recovery and reconstruction in the early years of the PRC. ● Despite the PRC being unable to tap into Soviet economic assistance immediately, mutual trade between China and the USSR nevertheless increased 6.5 times from 1950 to 1956. ● Together with the 50 projects promised by Stalin in 1950, the final version of the First FYP for the PRC included 141 Soviet and 68 East European projects in a total of 649 planned. Three thousand Soviet advisers sent to China in subsequent years were directly linked to the First FYP. ● By 1955, over 60 percent of China’s goods exchange was with the USSR. ● Soviet economic assistance to China added up to the largest foreign development venture in the socialist camp ever. ○ The total number of planned projects amounted to between 300 and 360 projects. ○ However, the number of total finished projects ranged between 134 and 150. ● Transfers of knowledge and expertise were important to China’s economic development. ○ A study on Soviet experts counts 1,445 political advisers and 9,313 technical specialists sent to China until their sudden withdrawal in mid-1960. ■ For political reasons, the gradual withdrawal of advisers began after late 1956.

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