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GEORGE and THE DRAGON 2
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Olly the Owl Bj, Story 3, George and the Dragon - 1st column Greek/EnglishOlly the Owl Bj, Story 3, George and the Dragon - 1st column English/GreekOlly the Owl Bj, Story 3, George and the Dragon - 1st column SCRAMBLEDA Brief History of Washington’s Crossing of the Delaware River, Christmas Night 1776... In the fall of 1776, General George Washington and his army had suffered a series of defeats at the hands of the British Army. The Continental Army had lost every battle with the British in the New York campaign: Long Island, Manhattan, Brooklyn Heights, Harlem and White Plains and had surrendered Fort Washington and Fort Lee. At Fort Lee, the army barely escaped and was forced to leave behind its store of provisions, ammunition, and many of its weapons. A sense of defeat had settled around Washington as he was forced to retreat across New Jersey in November and finally to Pennsylvania on December 8, 1776. The British, at least, considered the war over. By December 11th, the only reason the British had not taken Philadelphia, the seat of the Continental Congress, was that Washington had ordered every boat in the Delaware River on the New Jersey side to be brought to the Pennsylvania side, thus denying the British army transportation. Washington knew that the British would be capable of resuming an offensive by crossing the Delaware once it iced over. As the harsh winter set in, the morale of the American troops was at an all-time low. The soldiers were forced to deal with a lack of both food and warm clothing, while Washington watched his army shrink because of desertions and expiring enlistments. Now, more than ever, a victory was desperately needed. Washington devised a courageous plan to take the offensive and cross the Delaware River on Christmas night and attack the Hessian garrison at Trenton, New Jersey, nine miles south of his encampment near McConkey's Ferry. The original plan called for three divisions to cross the Delaware under the cover of darkness. Lt. Col. John Cadwalader's division was to cross at Bristol and engage the southern most contingent of British forces — Hessian troops under the command of Colonel von Donop. General James Ewing's division was to cross at Trenton Ferry and take a position south of Assunpink Creek below Trenton and hold the bridge over that stream. Washington's division was to cross at McConkey's Ferry and then divide into two corps under General Nathanael Greene and General John Sullivan. Their point of attack was Trenton and the Hessian troops quartered there under the command of Colonel Johann Gottlieb Rall. The boats to be used for the crossing were gathered earlier in the month in compliance with General Washington's orders, primarily as a defensive measure. Various types of boats had been collected, most notably the large Durham boats used to carry pig iron down the Delaware to the Philadelphia markets. There were a number of problems in moving a large number of men, cannons, and supplies in an age when overland transportation was by foot and animal power. The roads were rutted and winding. There were no bridges over major rivers because the technology did not exist to span great distances. A river like the Delaware was crossed by ferry, sometimes out of service because of ice floes or floods, and certainly not designed to carry masses of men and equipment across quickly. A river could be a formidable natural barrier to an army on the move. Washington had several logistical concerns for the crossing. In addition to the troops were the cannon; each of which required at least two horses to pull it. The heavier twelve pounders, and probably the eight pounders, had four horses. There would have been between four and six ammunitions wagons. Officers of the rank of colonel or higher may have had horses. In sum, Washington had to move 2,400 men, eighteen cannons, at least four ammunition wagons and fifty to seventy-five horses across the Delaware River the night of December 25, 1776. Fully expecting to be supported by Cadwalader's and Ewing's divisions south of Trenton, Washington assembled his own troops near McKonkey's Ferry in preparation for the crossing. By 6:00 pm, 2,400 men had begun crossing the ice-chocked river. There was an abrupt change in the weather, forcing the men to fight their way through sleet and a blinding snowstorm. The river was flooded with sheets of ice moving at eleven or twelve miles per hour. These obstacles proved to be too much for the two supporting divisions led by Generals Cadwalader and Ewing, who did not cross at their assigned points along the river. It was Washington's pure force of will and determination that led to his troops' successful crossing of the river. Increasing Washington's odds were the sailors of Marblehead, Massachusetts. This group of hardened seamen, led by Col. John Glover, were used to the Nor'easters of New England. Sheer determination and muscles conditioned to the demands of rowing under the weather conditions now facing the Continental army enabled the Marbleheaders to row back and forth across the Delaware countless times. During the time of the Revolution, American soldiers marched single file along the margins of the roads. They were only assembled into a battle line (three deep) when they reached the battlefield. The battle plan had Washington's army marching in two divisions... General Greene's and General Sullivan's. They made a night march in two columns on separate roads, a very tricky operation that was prone to failure since the columns needed to arrive at the battlefield at the same time to carry out the surprise attack planned by Washington. The American army carried out the march flawlessly. Against all odds, Washington and his men successfully completed the crossing and marched to Trenton on the morning of December 26th and, in the resulting battle, achieved a resounding victory over the Hessians. By moving ahead with his bold and daring plan, General Washington reignited the cause of freedom and gave new life to the American Revolution.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 briefly1. Battle of Lexington At the Battle of Lexington in 1775, British soldiers and colonial militia faced each other on the village green. A shot was fired, but no one knows for sure who fired first. Even so, this moment is often called the beginning of the American Revolution. Why is the Battle of Lexington still considered the start of the American Revolution, even though it is unclear who fired the first shot? A. It marked the first time colonists and British soldiers fought in open battle B. It proved that colonists planned the war long before the fighting began C. It showed that British soldiers were fully responsible for starting the war D. It confirmed that colonists had already declared independence from Britain 2. Battle of Concord After the fighting at Lexington, British troops marched to Concord to destroy colonial supplies. Instead, colonial militia gathered and fought back, forcing the British to retreat toward Boston. Why is the Battle of Concord considered an important turning point in the early American Revolution? A. It showed that colonial militias could organize and successfully push back British troops B. It proved that the British army had already lost control of all the colonies C. It confirmed that the colonies had officially declared independence from Britain D. It demonstrated that foreign countries were already helping the colonial forces 3. Second Continental Congress Much of the early violent conflict between colonists and British soldiers took place in Boston. After fighting broke out at Lexington and Concord near Boston, colonial leaders met at the Second Continental Congress in 1775 to decide what to do next. Which answer best describes the main actions taken by the Second Continental Congress? A. They created an army, chose a leader, and tried to avoid war with Britain B. They declared independence, wrote the Constitution, and ended the war C. They raised taxes, formed a monarchy, and supported British rule D. They ended slavery, gave women rights, and expanded voting laws 4. Olive Branch Petition In 1775, colonial leaders sent a letter called the Olive Branch Petition to King George III of Britain. Based on this situation, what was the main purpose of the Olive Branch Petition sent to the king? A. To ask the king to restore peace between both sides B. To declare independence from Britain and begin a new nation C. To request help from foreign countries in the war effort D. To organize protests against British taxes across the colonies 5. Battle of Bunker Hill On June 17, 1775, during the Battle of Bunker Hill in Boston, colonial forces fought against the British on a hill overlooking the city. The fighting was intense and led to heavy losses on both sides. Which statement best explains why the Battle of Bunker Hill was an important battle in the war? A. The colonists won the battle, showing they were stronger than British forces B. The colonists won the battle, showing the British that the war would be short and easy for the colonists C. The British won the battle, showing the war would be difficult and costly for both sides D. The British won the battle, showing British forces could defeat the colonists easily 6. Pamphlets During the American Revolution, pamphlets were short printed writings that were inexpensive to produce and often written in everyday language so many colonists could read them. How did these features of pamphlets most affect their role in the American Revolution? A. They helped spread ideas widely, allowing more colonists to form and share opinions B. They limited ideas to educated leaders, keeping most colonists uninvolved C. They replaced newspapers entirely, becoming the only source of information D. They prevented disagreement, causing most colonists to think the same way 7. Thomas Paine’s Common Sense In 1776, Thomas Paine published Common Sense, a widely read piece of writing about the relationship between the colonies and Britain. How did this pamphlet most influence colonial thinking during the American Revolution? A. It encouraged colonists to support independence from Britain B. It convinced colonists to remain loyal to the British government C. It explained how colonial armies should organize attacks D. It described laws colonists were expected to follow 8. Declaration of Independence In July 1776, the Declaration of Independence listed complaints against King George III and explained the colonists’ ideas about government and rights. How do these parts of the Declaration of Independence work together to support the colonists’ decision? A. They connect ideas about rights to real examples, justifying separation from Britain B. They describe past events in detail, showing how the war had already ended C. They list future plans for government, explaining how leaders would be chosen D. They organize military actions, showing how the colonies planned to win 9. Washington Crosses the Delaware and Battle of Trenton In December 1776, George Washington led his army across the Delaware River and launched a surprise attack on Hessian mercenaries in Trenton. Which statement best explains why Washington’s crossing of the Delaware and the attack on Trenton was an important turning point in the war? A. It defeated British forces completely, ending the war in a short time B. It boosted morale, helping discouraged soldiers choose to keep fighting C. It brought foreign allies into the war, adding support for the colonies D. It led to independence, allowing the colonies to form a new nation 10. Battle of Saratoga In 1777, American forces defeated the British at the Battle of Saratoga, a major event during the American Revolution. Which statement best explains why the Battle of Saratoga was an important turning point in the war? A. It brought French support, helping Americans gain a strong advantage in the war B. It ended the war quickly, forcing Britain to surrender all control in the colonies C. It improved army training, helping soldiers become more skilled in future battles D. It changed leadership roles, causing new generals to take control of the army 11. Battle of Yorktown In 1781, American forces surrounded British troops at Yorktown, leading to a major moment in the American Revolution. Which statement best explains why the Battle of Yorktown was an important event in the war? A. French forces helped the Americans win, leading to the end of major fighting in the war B. Italian forces helped the British win, leading to a final victory over the American army C. German forces switched sides and helped the Americans win, leading to a final defeat for British troops D. French forces helped the British win, leading to a complete end of the war in the colonies 12. Treaty of Paris After the Battle of Yorktown, British public opinion turned against the war, and peace negotiations began. In 1783, American leaders signed the Treaty of Paris, which included agreements between the United States and Britain. Which statement best explains how the Treaty of Paris reflected the outcome of the American Revolution? A. Both sides made agreements, recognizing independence B. Americans gained independence, taking land without agreements C. British leaders kept control, ending the war with power D. Both sides refused compromise, continuing the warThe motivations of George and Lennie in of Mice and MenThe Magic Cage George and Ginger read books in the gym about a magic cage. George can see a giant in a cage. Ginger finds a large gem on the giant. George and Ginger can see an angel do some magic.