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Intrinsic Semiconductors
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Intrinsic and Extrinsic Factors Affecting Microbial Growth in Food - Starter Quiz
Motivation: intrinsic and extrinsic
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There are 12 core values at BTS, with 4 core values being ânon-negotiablesâ. Each of the 12 core values are categorized into 3 main groups, Permission to Play, Architect of the Future, and Guardian of the Mood, to further encapsulate the broader aspects of BTS's work culture. The 4 non-negotiables: Being Super Hungry: This value underscores an intrinsic motivation and a relentless pursuit of goals. It reflects an individual's aspiration to continually strive for success, always seeking opportunities to grow and excel. Strong Willingness to Learn: This value promotes a continuous desire for personal and professional growth. It represents an open-minded approach to acquiring new skills and knowledge, which is critical in the ever-evolving field of taxation and financial services. Burning Desire for an Abundant Lifestyle: This value aligns well with the firm's vision and mission. It showcases a passionate pursuit of a prosperous life, not just in terms of financial wealth but a comprehensive approach to abundance, involving personal well-being and satisfaction. Burning Desire to be the Best: This embodies the drive to excel and be at the forefront in oneâs area of expertise. It encourages individuals to strive for excellence, setting the bar high and aiming to surpass it, fostering a culture of competitiveness and high performance. Permission to Play: This category delineates the foundational qualities BTS seeks in potential team members, reflecting a blend of passion, humility, presence, and aspiration for a prosperous life. Super Hungry: Being "Super Hungry" transcends personal ambition, creating an environment where passion and determination are contagious. It's about fostering an ecosystem of perpetual growth, where individuals are fervently working towards their goals while uplifting others. It represents a spirit of resilience and relentless forward motion, fostering a collective progress where success is a shared journey. Humble and Humility: Embracing humility is the cornerstone of personal and organizational growth at BTS. It encourages individuals to remain open to learning and receptive to constructive criticism, fostering a culture of continuous improvement. Humility embodies a willingness to relinquish ego, embracing the learnings that come through experiences and guidance. It cultivates a space where personal growth is accelerated through mutual respect and collaborative learning, ultimately paving the way for success. Burning Desire for an Abundant Lifestyle: This core value embodies a holistic pursuit of happiness, where individuals strive to find joy and fulfillment in various facets of life, including work, personal relationships, and mental well-being. It encourages a balanced approach to life, where passion for work aligns with personal joy, fostering a workplace where individuals are deeply committed and engaged in their roles, finding contentment and happiness in their professional pursuits. Being Fully Present and Inspiring: Being fully present encourages individuals to immerse themselves wholly in their tasks, minimizing distractions and maximizing productivity. It fosters a workplace where people are engaged, content, and genuinely invested in their roles. Simultaneously, nurturing an inspiring environment is about personal growth and self-motivation, where individuals are the driving forces behind their success, igniting inspiration through their journey and accomplishments, fostering a cycle of mutual motivation and growth. Architect of the Future: This category is about the cultivation of leaders within the team, encouraging qualities such as self-drive, innovation (revolutionist), a strong willingness to learn, and an unyielding desire to be the best in their field. Being Self-Driven: A self-driven individual embodies responsibility and initiative, equipped with a clear vision and a proactive approach to achieving their goals. They are fervent in bridging the gap between their present and envisioned future, fostering a goal-oriented mindset that is aggressive in its pursuit and focused on accomplishing its objectives. Being a Revolutionist: A revolutionist in the BTS context is an innovator, willing to defy conventional norms and embrace new approaches to foster growth and development. They are vocal advocates for change, bringing unique perspectives and solutions to the table, fostering an environment of innovation and progressive thinking. Even amidst resistance, they hold firm to their vision, aligning their actions with the core values and purpose that guide BTS's mission. Strong Willingness to Learn: An individual with a strong willingness to learn is adaptable, constantly evolving to meet the changing demands of the industry. They are voracious learners, continually seeking knowledge to enhance their expertise, thereby adding value to the clients and the organization. Burning Desire to be the Best: This value is about embodying excellence in every endeavor, fostering a culture where individuals are constantly striving to elevate their expertise and services. It encourages a proactive approach to personal and professional growth, where the quest for greatness is a continuous journey, propelled by learning and innovation. Guardian of the Mood: This focuses on maintaining a positive and collaborative work environment, emphasizing values such as gratefulness, patience, excitement, and helpfulness. It suggests that BTS values not only professional excellence but also emotional intelligence and positive interpersonal interactions. Being Grateful: Being grateful at BTS embodies a conscious appreciation of the opportunities and resources at hand. It encourages individuals to not just focus on personal milestones but to recognize and value the collective efforts and accomplishments of the team. It's about harboring a mindset of thankfulness that permeates everyday life, understanding that the privilege to progress and succeed is not to be taken for granted. This attitude fosters a nurturing environment where gratitude amplifies abundance, paving the way for more blessings and opportunities to flourish. Patience: Patience at BTS embodies a multifaceted approach that encompasses trust, readiness to play a role effectively, striving to reach one's potential, a hunger for success, and a helpful disposition. It encourages individuals to cultivate a patient attitude, fostering a work environment where goals are pursued with persistence and determination. Genuine Excitement: Genuine excitement at BTS manifests as a contagious enthusiasm that permeates the organization. It is characterized by a deep-seated passion for one's work, fostering a positive and vibrant work environment where individuals are energized and motivated to make a meaningful impact through their roles. Being Helpful: Being helpful at BTS entails proactively identifying opportunities to assist, be it in aiding clients with their concerns or supporting team members in their roles. It fosters a collaborative and supportive work environment, where individuals are attuned to the needs of others and are ready to step in to provide assistance.
Long Call Option Trading Strategy: Learn the Basics LONG CALL SUMMARY Purchasing a call option is a bullish strategy that gives the buyer the right, but not the obligation, to buy 100 shares of the underlying asset at a specified strike price on or before the expiration date. This strategy is typically employed when an investor believes that the price of the underlying asset will increase in the future. The value of a call option is influenced by several factors, including the underlying asset's price, the strike price, the time to expiration, and implied volatility. As the price of the underlying asset increases and approaches or breaches the long call's strike price, the option's value will appreciate. This is because the option holder has the right to buy the underlying asset at a lower price than the current market price, resulting in a potential profit. Out-of-the-money (OTM) calls have a strike price that is higher than the current market price of the underlying asset. These options are typically cheaper than in-the-money (ITM) calls, which have a strike price lower than the current market price. ITM calls have intrinsic value, which is the difference between the strike price and the current market price, and extrinsic value, which is the additional premium paid for the option's time value. Extrinsic value decays over time as the option approaches expiration, and this can cause the option to lose value, especially if the underlying asset does not move towards the strike price. LONG CALL OPTION Purchasing a call option grants you the privilege, but not the responsibility, to buy 100 shares of the underlying asset at the specified strike price on or before the expiration date. This option grants you the flexibility to capitalize on potential price increases of the underlying asset. The value of a call option is positively correlated with the price of the underlying asset. As the price of the stock or ETF rises and approaches your strike price, the value of your call option increases. This is because the difference between the market price and the strike price widens, giving you a greater potential profit. This characteristic makes call options suitable for bullish strategies where investors anticipate price increases. Conversely, the value of a call option diminishes when the price of the underlying asset drops or remains constant. Time decay, which refers to the gradual loss of an option's value as its expiration date approaches, also contributes to the depreciation of call options. Over time, the intrinsic value of the option, which represents the difference between the strike price and the underlying asset's market price, decreases as the option nears expiration. Additionally, if the price of the underlying asset remains below the strike price, the option may expire worthless, resulting in a total loss of the premium paid. Understanding these dynamics is crucial when trading call options. It allows you to make informed decisions about when to enter and exit positions, taking into account factors such as the underlying asset's price movements, time decay, and market sentiment. Buying call options can provide an alternative strategy to gain long exposure to a stock's price movement without the need for purchasing shares directly. This approach, known as a long call position, offers the potential advantage of lower capital outlay compared to buying shares outright. However, it's crucial to understand the concept of time decay, which significantly impacts the value of long call options. Time decay refers to the gradual decrease in the value of an option as time passes. This phenomenon occurs due to two primary factors: theta and vega. Theta measures the rate at which an option's value decays over time, while vega measures the sensitivity of an option's price to changes in implied volatility. As the expiration date of the call option approaches, both theta and vega work together to erode the option's value. Consequently, to offset the impact of time decay, the underlying stock price must rise at a greater velocity towards the call option's strike price. This is because the intrinsic value of a call option, which represents the difference between the strike price and the underlying stock's current market price, increases as the stock price moves higher. Another important consideration when evaluating call options is the distinction between out-of-the-money (OTM) and in-the-money (ITM) calls. OTM calls have a strike price higher than the current market price of the underlying stock, while ITM calls have a strike price lower than the current market price. OTM calls are typically less expensive than ITM calls because their value is composed entirely of extrinsic value. Extrinsic value refers to the portion of an option's price that is not attributable to its intrinsic value. ITM calls, on the other hand, have both intrinsic and extrinsic value, resulting in a higher cost per contract. As time relentlessly marches forward, the value of call options undergoes a transformation. The extrinsic value, which represents the premium paid for the potential of future price movements, steadily diminishes as expiration approaches. This decay is universal, affecting all call options regardless of their initial strike price or distance from the underlying asset's current price. However, amidst this gradual erosion of extrinsic value, ITM (in-the-money) call options stand as an exception. These options retain their intrinsic value at expiration, which is the difference between the strike price and the underlying asset's price. This characteristic sets ITM call options apart from their OTM (out-of-the-money) counterparts, whose extrinsic value decays entirely to zero near or at expiration. The distinction between ITM and OTM call options underscores the significance of carefully considering both the time frame and strike price when making investment decisions. Traders seeking to maximize their potential gains through call options must be mindful of the impending decay of extrinsic value as expiration draws near. For long ITM call options, the ideal scenario is for the underlying asset to exhibit a significant upward movement. Such a price increase would enhance the intrinsic value of the option, making it worth more at expiration than the initial purchase price. This scenario holds true for OTM call options as well, as they require the underlying asset to move ITM at expiration to possess any value. Prior to expiration, both OTM and ITM call options have the potential to gain a combination of extrinsic and intrinsic value if the stock exhibits a rapid upward trajectory. This dynamic underscores the importance of monitoring market conditions and adjusting investment strategies accordingly. Understanding the Interplay of Time, Strike Price, and Option Value in Call Option Trading: In the realm of call option trading, comprehending the intricate interplay between time, strike price, and option value is paramount to success. These three factors collectively shape the dynamics of call option contracts, allowing traders to make informed decisions and capitalize on market opportunities. Time (Days to Expiration): Time, measured in days until expiration, is a crucial element in call option trading. As expiration approaches, the value of a call option is directly influenced by the time premium. The closer an option gets to expiration, the less time value it holds. This time decay accelerates in the final days leading up to expiration. Therefore, traders must carefully consider the time factor when selecting their expiration dates. Strike Price: The strike price represents the predetermined price at which the underlying asset can be bought (in the case of a call option) or sold (in the case of a put option). When choosing a strike price, traders must assess the current market price of the underlying asset and make an educated guess about its future direction. ITM (In-the-Money) call options are those with a strike price below the current market price, while OTM (Out-of-the-Money) call options have a strike price above the current market price. Option Value: Option value refers to the premium paid by the buyer of an option contract to the seller. This premium comprises two components: intrinsic value and time value. Intrinsic value is the difference between the strike price and the underlying asset's current market price. Time value, as mentioned earlier, is the premium paid for the remaining time until expiration. Auto-Exercise and Expiration Scenarios: Auto-Exercise: Long call options that expire ITM by $0.01 or more will be automatically exercised. This means that the buyer of the call option has the right to purchase the underlying asset at the strike price. If the investor holds only a long call, this will result in 100 long shares per contract purchased at the call option's strike price. On the other hand, investors holding the corresponding short shares will cover or buy shares at the call option's strike price. Expiration Worthless: Any long call options that expire OTM will expire worthless. In this scenario, the investor loses the entire premium paid for the contract, resulting in a maximum loss. Understanding these concepts is instrumental in developing effective call option trading strategies. By carefully considering the interplay between time, strike price, and option value, traders can position themselves to make profitable trades and minimize potential losses. PROFIT & LOSS DIAGRAM OF A LONG OTM CALL A long OTM call option can be profitable if the current market value of the option exceeds the price paid to purchase it. This can occur in two main scenarios: Stock Price Surpasses Strike Price: If the underlying asset's price rises above the strike price of the call option by more than the premium paid for the option, the call option becomes profitable. This is because the intrinsic value of the call option (the difference between the strike price and the underlying asset's price) becomes positive, and the call option can be exercised to purchase the underlying asset at a price below the market price. OTM Call Moves Closer to Underlying Asset Price: Even if the underlying asset's price does not reach the strike price, a long OTM call can still be profitable if the option's price increases. This can happen when there is a quick rally in the underlying asset's price, causing the call option's price to increase as well, even if the strike price is not reached. This is because the time value of the call option increases as the expiration date approaches, and the call option becomes more likely to be in the money. However, it's important to note that long OTM call options can also result in losses if the underlying asset's price does not surpass the breakeven point. The breakeven point is the price at which the call option's intrinsic value becomes equal to the purchase price of the option. If the underlying asset's price remains below the breakeven point until expiration, the call option will expire worthless, and the investor will lose the entire amount paid for the option. The maximum profit potential of a long OTM call option indeed has no theoretical limit, as a stock's price can theoretically rise indefinitely. This means that if the underlying stock price increases significantly, the call option holder can potentially reap substantial profits by exercising the option and buying the stock at the predetermined strike price. On the downside, the maximum loss on a long call option is limited to the premium paid for the option. This premium represents the total amount invested in the option contract and acts as a protective barrier against further losses. If the stock price declines or stays below the strike price at expiration, the option will expire worthless, and the investor will lose the entire premium paid. The flattened red loss zone in the diagram illustrates this limited loss potential. This zone represents the range of stock prices below the strike price at expiration where the option holder will lose money. The loss amount decreases as the stock price approaches the strike price and becomes zero when the stock price equals the strike price. Beyond the strike price, the option holder starts to make a profit. It's important to note that while the maximum profit potential is theoretically unlimited, it is highly unlikely for a stock price to rise dramatically within the short timeframe of an OTM option's expiration period. Therefore, while the potential rewards can be significant, the probability of achieving them is relatively low. PROFIT & LOSS DIAGRAM OF A LONG ITM CALL ITM (In-the-Money) options have a unique characteristic where the price of their intrinsic value directly correlates with the underlying asset's price. This means that for every one point movement in the underlying asset's price, the ITM option's intrinsic value moves by the same amount. While purchasing an ITM option provides immediate intrinsic value, it does not guarantee profitability upon execution. Similar to buying an OTM (Out-of-the-Money) call option, the purchase price of an ITM call must increase for it to be profitable. This requires the stock price to move further above the call strike price. This relationship is visually represented in the diagram, where the red and green zones converge on the x-axis. The maximum potential loss on a long call option is limited to the debit paid for the option, which is represented by the flattened red area in the diagram. This means that the most an investor can lose on a long call is the premium paid for the option, regardless of how far the underlying asset's price moves below the strike price. Understanding the price dynamics and potential risks associated with ITM options is crucial for traders and investors. While ITM options offer immediate intrinsic value, careful analysis and consideration of market conditions are necessary to determine their potential profitability. EXAMPLE OF A LONG OTM CALL OPTION XYZ currently trading @ $45 Buy to Open +1 XYZ 50-strike call @ $4 debit Cost: $4 debit ($400 total, ($4 x 100 shares)) Time Decay Affect Works against the optionâs value Max Profit Theoretically unlimited Max Loss Debit paid per contract ($400) Breakeven Price (at expiration) Strike price + debit paid ($54) Account Type Required Cash, Margin, and IRA EXAMPLE OF A LONG ITM CALL OPTION XYZ currently trading @ $45 Buy to Open +1 XYZ 40-strike call @ $7 debit ($5 intrinsic value + $2 extrinsic value) Cost: $7 debit ($700 total) Time Decay Affect Works against the optionâs value Max Profit Theoretically unlimited Max Loss Debit paid per contract ($700) Breakeven Price (at expiration) Strike price + debit paid ($47) Account Type Required Cash, Margin, and IRA
Nutrition, Metabolism, and Body Temperature Regulation. Nutrient is a substance that promotes normal growth, maintenance, and repair. Major nutrients are carbohydrates, lipids, and proteins. Other nutrients include vitamins and minerals (and technically speaking, water).Complex carbohydrates (starches) are found in bread, cereal, flour, pasta, nuts, and potatoes .Simple carbohydrates (sugars) are found in soft drinks, candy, fruit, and ice cream.Glucose is the molecule ultimately used by body cells to make ATP.Neurons and RBCs rely almost entirely upon glucose to supply their energy needs.Excess glucose is converted to glycogen or fat and stored .The most abundant dietary lipids, triglycerides, are found in both animal and plant foods.Essential fatty acids â linoleic and linolenic acid, found in most vegetables, must be ingested. Dietary fats help the body to absorb vitamins, a major energy fuel of hepatocytes and skeletal muscle, and a component of myelin sheaths and all cell membranes. Lipids functions in smooth muscle contraction, control of blood pressure and inflammation. Cholesterol stabilizes membranes and is a precursor of bile salts and steroid hormones. The dietary requirements for lipids are higher for infants and children than for adults. The American Heart Association suggests that fats should represent less than 30% of oneâs total caloric intake, saturated fats should be limited to 10% or less of oneâs total fat intake, and daily cholesterol intake should not exceed 200 mg. Complete proteins that meet all the bodyâs amino acid needs are found in eggs, milk, milk products, meat, and fish.Incomplete proteins are found in legumes, nuts, seeds, grains, and vegetables. Essential amino acids are the building blocks for nonessential amino acids. Protein supply for nonprotein nitrogen-containing substances. Daily intake should be approximately 0.8g/kg of body weight. All amino acids needed must be present at the same time for protein synthesis to occur. Protein will be used as fuel if there is insufficient carbohydrate or fat available. The rate of protein synthesis equals the rate of breakdown and loss. Anabolic hormones accelerate protein synthesis. Vitamins are organic compounds needed for growth and good health. They are crucial in helping the body use nutrients and often function as coenzymes. Only vitamins D, K, and B are synthesized in the body; all others must be ingested. Water-soluble vitamins (B-complex and C) are absorbed in the gastrointestinal tract . Vitamin B12 additionally requires gastric intrinsic factor to be absorbed. Fat-soluble vitamins (A, D, E, and K) bind to ingested lipids and are absorbed with their digestion products. Vitamins A, C, and E also act in an antioxidant cascade. There are seven minerals are required in moderate amounts . These are calcium, phosphorus, potassium, sulfur, sodium, chloride, and magnesium. Dozens are required in trace amounts. Minerals work with nutrients to ensure proper body functioning. Calcium, phosphorus, and magnesium salts harden bone.
Influence of China and India China ChinaChina under the Han emperor Wudi (c. 100 bce) and (inset) at the end of the Chunqiu (Spring and Autumn) Period (c. 500 bce). Between approximately 150 bce and 150 ce, most of Southeast Asia was first influenced by the more mature cultures of its neighbours to the north and west. Thus began a process that lasted for the better part of a millennium and fundamentally changed Southeast Asia. In some ways the circumstances were very different. China, concerned about increasingly powerful chiefdoms in Vietnam disturbing its trade, encroached into the region and by the end of the 1st century bce had incorporated it as a remote province of the Han empire. For generations, the Vietnamese opposed Chinese rule, but they were unable to gain their independence until 939 ce. From India, however, there is no evidence of conquests, colonization, or even extensive migration. Indians came to Southeast Asia, but they did not come to rule, and no Indian power appears to have pursued an interest in controlling a Southeast Asian power from afar, a factor that may help to explain why only the Vietnamese accepted the Chinese model. Yet, in other ways the processes of Indianization and Sinicization were remarkably similar. Southeast Asia already was socially and culturally diverse, making accommodation easy. Furthermore, indigenous peoples shaped the adaption and adoption of outside influences and, indeed, seem to have sought out concepts and practices that enhanced rather than redirected changes already underway in their own societies. They also rejected some components: for example, some of the vocabulary and general theories related to the Indian notions of social hierarchy were borrowed but much of the specific practices were not, and neither Indian nor Chinese views of women as socially and legally inferior were accepted. In the later stages of the assimilation processâparticularly in the Indianized areasâlocal syncretism often produced exuberant variations, which, despite familiar appearances, were expressions of local genius rather than just inspired borrowings. Get Unlimited Access Try Britannica Premium for free and discover more. Sculptures at Borobudur, central Java, Indonesia. 1 of 2 Sculptures at Borobudur, central Java, Indonesia. Pagan, Myanmar 2 of 2 Pagan, MyanmarRuins of ancient Buddhist shrines and pagodas, Pagan, Myanmar. Still, Chinese and Indian influences were anything but superficial. They provided writing systems and literature, systems of statecraft, and concepts of social hierarchy and religious belief, all of which were both of intrinsic interest and pragmatic significance to Southeast Asians of the day. For elites seeking to gain and retain control over larger and more complex populations, the applications of these ideas were obvious, but it would also seem that the sheer beauty and symbolic power of Hindu and Buddhist arts tapped a responsive vein in the Southeast Asian soul. The result was an imposing array of architectural and other cultural wonders, at first very much in the Indian image and hewing close to current styles and later in more original, indigenous interpretations. The seriousness and profundity with which all this activity was undertaken is unmistakable. By the 7th century ce, Palembang in southern Sumatra was being visited by Chinese and other Buddhist devotees from throughout Asia, who came to study doctrine and to copy manuscripts in institutions that rivaled in importance those in India itself. Later, beginning in the 8th century, temple and court complexes of surpassing grandeur and beauty were constructed in central Java, Myanmar, and Cambodia; the Borobudur of the Ćailendra dynasty in Java, the myriad temples of the Burman dynastic capital of Pagan, and the monuments constructed at Angkor during the Khmer empire in Cambodia rank without question among the glories of the ancient world.
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, âŠ. 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, âŠ, n â 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 Ï 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 â l â 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 â 0 â 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 â 0 â 1 = 1 node for 2s, and 3 â 0 â 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 â 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 â1, 0, or +1. Generally speaking, ml can be equal to âl, â(l â 1), âŠ, â1, 0, +1, âŠ, (l â 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 â„ 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 electronâelectron 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 ârotationâ or âspinning.â 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 âspinâ 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 ÎČ state, with the z component of the spin being negative and ms=â12. 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=â12 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 â12. 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=â12 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