Shells and subshells

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

WHAT IS SCIENCE? - is a way in which answers related to NATURAL events are proposed. - a way in which people can learn and UNDERSTAND events in the NATURAL WORLD - based on OBSERVABLE EVENTS - a study of the NATURAL WORLD - a method of DISCOVERY and UNDERSTANDING by using a PROBLEM-SOLVING process called the?? - A systematic body of knowledge based on observation and experimentation. FOUR COMMON CHARACTERISTICS OF SCIENCE: 1. It focuses on the NATURAL WORLD. 2. Goes through experiment. 3. Relies on evidence. 4. Passes through the scientific community. WHAT IS TECHNOLOGY? Brian Arthur (2009) defined technology as: 1. a means to fulfill a human purpose 2. assemblage of practices and components 3. a collection of devices and engineering practices available to a culture. SOCIETY ST (Science Technology) would not exist without society. WHAT IS STS? Science and Technology and Society (STS) is the study of how society, politics and culture affect scientific research and technological innovation and how these, in turn affects society, politics and culture. EVENTS IN THE HISTORY OF SCIENCE AND TECHNOLOGY THAT TRANSFORMED THE SOCIETY (IN THE WORLD) ANCIENT PERIOD 3500 BC. - 500 AD EUROPE - use of fire by Homo Erectus CA 750,000 - Stone Headed Spears CA 45,000 - Wooden bow and arrow CA 20,000 - The Minoans build palaces in Crete CA 2,000 THE AMERICAS - The Folsom people living on eastern side of the Rocky Mountain developed sophisticated tools CA 8,000. - Pottery is made in South America CA 6,000 - Olmec sculpture carves figurines and giant human heads. CA 1200 ASIA AND OCEANA - Earliest known clay pots are made in Japan CA 11,000. - Bronze is first made in Thailand CA 4000 - A lunar calendar is developed in China CA 2950 - Chinese doctors begin using acupuncture CA 2500 - The Hindu calendar of 360 days was introduced in India CA 1000 AFRICA AND MIDDLE EAST - Homo erectus uses stone tools CA 1000000 - CA 15000 in Africa, bone harpoons are used for fishing. - Clay tokens are used for record keeping in Mesopotamia CA 7500 - Mesopotamian mathematicians discover the Pythagorean Theorem MEDIEVAL PERIOD CA 500 -1500 - Dark ages because few written records and evidences remained - Scholastic tradition was established by Charlemagne - Vertical windmills, spectacles, mechanical clock, water mills, gothic style were invented - Johannes Gutenberg invented the printing press RENAISSANCE PERIOD 14TH – 17TH CENTURY - Rebirth of revival - Printing with movable type allowed Bible, secular books made in large amount - Nicolas Copernicus presented a heliocentric theory - Galileo Galilei invented telescope INDUSTRIAL REVOLUTION 18TH CENTURY - Skilled workers were set aside because of the machines - Iron production, steam engine and textile flourished - Scottish James Watt improved steam engine Robert Fulton (steam boat) - The following were invented: Light bulb, telephone, first steam powered locomotive 19TH CENTURY - Age of machine and tools - Herman Helmholtz (law of conservation of energy) - James Clark Maxwell (light as electro-magnetic wave) - Henry Becquerel (radioactivity) - Marie and Pierre Curie (radium) - Hans Christian Oersted (electric current near the magnet) - Michael Faraday (magnet produces electricity) - Atomic Theory proposed by John Dalton - Electron discovered by JJ. Thomson - Telegraph developed by Samuel Morse 20TH CENTURY - Communication, transportation, military research were developed - Personal computer was created - Intel developed microprocessor - Apple was introduced by Steve Jobs and Steve Wozniak - Internet was created (ARPANET) - Henry Ford's mass production of cars - Artificial Intelligence was invented SCIENCE, TECHNOLOGY AND SOCIETY (PHILIPPINE HISTORY) Stone Age - Archeological findings show that modern man from Asian mainland first came over land on across narrow channels to live in Batangas and Palawan about 48,000 B.C. - Subsequently they formed settlement in Sulu, Davao, Zamboanga, Samar, Negros, Batangas, Laguna, Rizal, Bulacan and Cagayan. Inventions - They made simple tools and weapons of stone flakes and later developed method of sawing and polishing stones around 40,000 B.C. - By around 3,000 B.C. they were producing adzes ornaments of seashells and pottery. Pottery flourished for the next 2,000 years until they imported Chinese porcelain. Soon they learned to produce copper, bronze, iron, and gold metal tools and ornaments. Iron Age - The Iron Age lasted from the third century B.C. to 11th century A.D. During this period Filipinos were engaged in extraction smelting and refining of iron from ores, until the importation of cast iron from Sarawak and later from China. INVENTIONS AND DISCOVERIES - They learn to weave cotton, make glass ornaments, and cultivate lowland rice and dike fields of terraced fields utilizing spring water in mountain regions. - They also learned to build boats for trading purposes. - Spanish chronicles noted refined plank built warships called caracoa suited for interisland trade raids 10TH CENTURY A.D. - Filipinos from the Butuan were trading with Champa (Vietnam) and those from Ma-I (Mindoro) with China as noted in Chinese records containing several references to the Philippines. These archaeological findings indicated that regular trade relations between the Philippines, China and Vietnam had been well established from the 10th century to the 15th century A.D. TRADING - The People of Ma-I and San-Hsu (Palawan) traded bee wax, cotton, pearls, coconut heart mats, tortoise shell and medicinal betel nuts, panie cloth for porcelain, leads fishnets sinker, colored glass beads, iron pots, iron needles and tin. SOME PRESPANISH FILIPINO SCIENCE AND TECHNOLOGY - Curative values of plants extract use as medicine - Alphabet (Alibata) - Counting Methods - Weights - Measuring system (isang gatang) - Calendar based on the periods of moon - Banaue Rice Terraces SPANISH REGIME  Religion the Catholic Church - The latter part of the 16th Century Development of schools: - Colegio de San Ildefonso-Cebu-1595 - Colegio de San Ignacio-Manila-1595 - Colegio De Nuestra Senora del Rosario-Manila 1597 - Colegio De San Jose-Manila-1601  Colegio De San Ildefonso De Cebu - In 1863 the colonial authorities issued a royal degree to reform the existing educational system. In 1871 the school of medicine and pharmacy were opened to UST, after 15 years it had granted the degree Of Licenciado En Medicina to 62 graduates.  Medicine - Development of hospitals San Juan Lazaro hospital the oldest in the far east was founded in 1578.  Roads and Bridges Among other Spanish contributions: - Arithmetic - Algebra - Geometry - Trigonometry - Physics - Hydrography - Meteorology - Navigation - Pilotage American Period and Post Commonwealth Era - BUREAU OF GOVERNMENT LABORATORIES (1901) - BUREAU OF SCIENCE (1905) - INSTITUTE OF SCIENCE (1946) RA 2067 OTHERWISE KNOWN AS THE “SCIENCE ACT OF 1958”. - This was enacted to integrate, coordinate, and intensify scientific and technological research and development and to foster invention including allocation of funds and other purposes. NATIONAL RESEARCH COUNCIL WAS ESTABLISHED ON DECEMBER 8, 1933. - Its Mandate (Nrcp) Promotes And Supports Fundamental Or Basic Research For The Continuing Total Improvement Of The Research Capability Of Individual Scientists Or Group Of Scientists; Provides Advice On Problems And Issues Of National Interest; Promotes Scientific And Technological Culture To All Sectors Of Society; And Fosters Linkages With Local And International Scientific Organizations For Enhanced Cooperation In The Development And Sharing Of Information NATIONAL RESEARCH COUNCIL WAS ESTABLISHED IN DECEMBER 8, 1933. - Its Mandate (NRCP) promotes and supports fundamental or basic research for the continuing total improvement of the research capability of individual scientists or group of scientists; provides advice on problems and issues of national interest; promotes scientific and technological culture to all sectors of society; and fosters linkages with local and international scientific organizations for enhanced cooperation in the development and sharing of information. It was during the American Period when Science was inclined towards: - Agriculture - Food Processing - Forestry - Medicine - Pharmacy - Nursing

Shells and Terminals in Linux

Electron Shells and Emission Spectra

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Atoms and electron shells

Science Exam Parts of the Atom: The atom consists of a nucleus at its center, containing protons (positively charged) and neutrons (neutral), while electrons (negatively charged) orbit in electron shells around the nucleus. Atomic Number: The atomic number of an element is the number of protons in its nucleus. It defines the element and determines its place on the periodic table. Properties of Metals: Metals have properties like conductivity, malleability (can be flattened into sheets), and ductility (can be drawn into wires). Elements, Compounds, and Mixtures: Elements consist of only one type of atom. Compounds are made of two or more different elements chemically bonded. Mixtures are combinations of substances that are physically mixed but not chemically bonded. Homogeneous and Heterogeneous Mixtures: Homogeneous mixtures have a uniform composition (e.g., saltwater), while heterogeneous mixtures have different phases (e.g., oil and water). Changes of State: Changes like melting, evaporation, and condensation are examples of physical changes of state. Chemical and Physical Properties: Chemical properties describe how a substance can change to form a new substance, while physical properties are characteristics like color, texture, and state (solid, liquid, gas). Physical and Chemical Change: A physical change involves the appearance or state of matter, but the substance remains the same. A chemical change involves the formation of new substances. Chemical Equations: Chemical reactions can be represented with chemical equations that show reactants (what you start with) and products (what is formed). Chemical Formulas: Chemical formulas represent the composition of compounds. For example, NaHCO3 is sodium bicarbonate, consisting of one sodium (Na), one hydrogen (H), one carbon (C), and three oxygen (O) atoms. Energy: Types of Energy: Energy can be kinetic (related to motion), potential (stored energy), thermal (heat energy), electrical, chemical, and more. Units of Energy: Common units of energy include joules (J) and calories (cal). Law of Conservation of Energy: Energy cannot be created or destroyed, only transferred or transformed from one form to another. Energy Transfer and Transformation: Energy moves from one object to another, changing forms along the way. Useful and Waste Energy: Useful energy is what can be harnessed and used for a specific purpose. Waste energy is energy that is not used and is often lost. Energy Flow Diagrams: These diagrams show how energy is transferred or transformed within a system. Energy Efficiency: Efficiency is a measure of how much useful energy is obtained from a system. It can be calculated using the equation: Efficiency = (Useful Energy Output / Total Energy Input) x 100%. Fossil Fuels and Renewable Energy: Fossil fuels, like coal, oil, and natural gas, are non-renewable sources of energy. Renewable energy sources include solar, wind, and hydroelectric power. Variables: Independent Variable: The variable that is manipulated or changed in an experiment. Dependent Variable: The variable that is measured or observed and is affected by changes in the independent variable. Controlled Variables: Factors that are kept constant to ensure a fair and accurate experiment.

The following days are a jumble of gunfire, digging, gobbled food, soldiers running in and out of the forest in small groups, distant explosions, stray shells, bandaged heads and unexpected lulls. On the very first day, before dawn, I am ordered into one of the newly dug trenches. I huddle there, squeezing my magic buttons and singing songs to the dog. When the fighting stops, the dog disappears, but a new companion takes his place. A strange little soldier crawls along the trench toward me. ‘Private Sasha!’ he cries. ‘I’ve been looking for you all day long!’ He’s old, like a grandfather, a dedushka. He has a black patch over one eye, a tape measure around his neck and a row of pins threaded into his sleeve. Hanging from his belt is the most enormous pair of scissors I have ever seen and I wonder if he uses them as a weapon. He doesn’t tell me his name, so in my head he becomes Dedushka. Dedushka squats, cups his hand to his ear, peers over the top of the trench and smiles. ‘It’s safe to be upright . . . for now.’ He helps me to my feet, dusts me off and commands me to stand as tall and straight as I can. Then he measures me. Everything from head to toe – even my toes! He writes numbers in a little notebook, strings his tape measure back around his neck, salutes and hurries away. It’s all very strange, and I wonder if Dedushka has been bumped on the head during the battle and is now a little bit muddled. I should have given him a hug before he left. I chase after him but stop when I’m hit by a shovelful of flying dirt. Sleepy Bear is digging a cave! ‘Are you going to hibernate?’ I ask. Sleepy Bear chuckles. ‘No, although that would be wonderful! I could do with a lo-o-o-ong sleep.’ He sighs and closes his eyes. He doesn’t open them again and I realise that he has gone to sleep. Standing up! I shake his arm, and he opens his eyes and keeps talking. ‘No, I’m not hibernating. I’m digging a little nook where I can sleep and eat. I’ll hang up my raincape as a door that can open and close so it feels just like a real home . . . except for the lice . . . and the bad smells . . . and the bombs that make the walls shake and crumble.’ He points further along the trench to where other soldiers are digging. ‘We’re all making little houses in the ground.’ ‘Like rabbits and moles,’ I say. Sleepy Bear chuckles. ‘Yes! And soldiers who need to hide from German bullets and bombs.’ He stops digging to roll a cigarette. ‘Should I be making a house?’ I ask. ‘I want to hide from German bullets and bombs, too.’ Sleepy Bear flops to the ground, lights his cigarette, closes his eyes and takes a deep puff. I wait for him to answer, but, instead, he begins to snore! I poke him in the side. He snorts and he murmurs, ‘I think someone has already built you a house, Sasha. Keep going along this beautiful village street and you are sure to find it.’ He falls asleep once more. I kiss his dusty cheek and whisper, ‘Thank you, Sleepy Bear.’ A little way along, I see Cook in a cloud of smoke. He has lit a fire, right here in the middle of the trench, and is stirring a cauldron full of kasha. He squats as he stirs. ‘What are you doing?’ I ask. ‘Cooking supper, of course!’ he cries. ‘But why are you doing it here?’ Cook points his spoon at the ground above the trenches. ‘Because if I do it up there, my pot will be filled with holes from German bullets and all of the kasha will leak out onto the ground. It’s bad enough that our supplies can’t get through German lines and there’s nothing to cook but buckwheat for kasha. But if we lost the kasha, too . . .’ ‘Hungry soldiers,’ I say. Cook nods. ‘And grumpy!’ ‘Like Boris!’ I gasp. ‘Even worse,’ warns Cook. I picture the kasha pot full of bullet holes. And then I realise that if the kasha pot were full of holes, then Cook would be, too. I wrap my arms around Cook’s neck and say, ‘I think this is a very good place for cooking our supper.’ I kiss his smoky cheek and run along. At the end of the trench, I find the biggest hole of all. It’s wide and deep and as busy as a beehive in a blossom tree. Above, a group of soldiers is rolling logs into place for a roof, while below, typewriters rattle and pencils scratch and papers flutter and voices crackle out of five different radios. Their words tangle together to tell a strange wartime fairy tale about German guns and a loving father called Stalin and a Red Army regiment that is lost in the deep, dark forest and a wicked beast called Hitler and a delivery of vegetables that was hit by a bomb and blown into a million tiny pieces too small even to make soup. In the middle of it all, wrestling with a rumpled map, his rifle still slung over his shoulder, is Major Scruff. ‘Major Scruff!’ I run and jump into his arms. ‘Is this our new home?’ ‘Yes, Sasha. I suppose it is.’ ‘Is it safe from German bullets and bombs?’ I ask. He stares at me. ‘Were you scared in the trenches today, Sasha?’ ‘No,’ I reply. ‘I had magic buttons and a dog and some songs to sing. Were you scared in the forest, Major Scruff?’ ‘Yes,’ he says. ‘Poor Major Scruff!’ I press my hand against his cheek. The dark, rough stubble is grubby with grit and his eyelids are taking a long time to open after every blink. ‘You need a shave and a nap!’ I scold. He chuckles. ‘I am too tired to shave and too busy to nap.’ I scrunch my nose while I consider his problem. ‘I know!’ I cry. ‘You nap and I will shave your whiskers. That will be two jobs tumbled into one!’ And so that’s what we do. Major Scruff slumps into a chair and snoozes while I lather his face with soapy water and shave his whiskers. The soap suds travel from his face, up into his hair and down the front of his uniform, and I have to shave his jaw and chin three times because I keep missing bits, but I finally get it all done. I am just wiping his cheeks dry when the dog appears. He licks my hand, then stretches up and licks soap suds from Major Scruff’s ear. Major Scruff wakes with a start. He feels his newly shaved face and cries, ‘Wonderful, Sasha! I feel smooth, clean, rested and ready for action.’ He ruffles my hair. ‘We must do this again tomorrow. Although next time, you might wake me with a gentle shake of the shoulder instead of licking my ear.’

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