Bohr Atomic Model, Lewis Structures, Chemical Bonding, and Newton's Laws of Motion Study Guide

Electronic Configuration According to the Bohr Model

The Bohr model describes the distribution of electrons within an atom across different energy levels. Level 1, also designated as the K shell, can accommodate a maximum of $2$ electrons. Level 2, or the L shell, has a maximum capacity of $8$ electrons. Level 3, the M shell, can hold up to $18$ electrons. For the specific example of Strontium ($Sr$), which has an atomic number ($Z$) of $38$, the electronic distribution is calculated by filling these levels sequentially. Since the sum of electrons in the first three levels ($2 + 8 + 18$) equals $28$, the remaining $10$ electrons are placed in Level 4, known as the N shell. Thus, the configuration for Strontium is represented as Nivel 1 (K): $2$, Nivel 2 (L): $8$, Nivel 3 (M): $18$, and Nivel 4 (N): $10$. The fundamental expression used to determine the maximum number of electrons for any energy level ($n$) in the Bohr model is $2n^2$. Under this model, when an electron transitions from a lower energy orbit to a higher energy orbit, it must absorb energy. Conversely, Bohr introduced the postulate that electrons can only orbit in specific, quantified energy levels rather than at any arbitrary distance from the nucleus.

Valence Electrons and Lewis Structures

The development of the periodic table and the concept of electronic configuration provided the foundation for understanding molecule and compound formation. Gilbert N. Lewis proposed that atoms combine to achieve a more stable electronic configuration, with maximum stability reached when an atom possesses a configuration similar to that of a noble gas. This stable state usually involves having eight electrons in the outermost shell, a principle known as the octet rule, formulated by Lewis and Langmuir. Only the electrons in the outermost regions, known as valence electrons, are involved in chemical bonding. Edward Frankland first mentioned the "combining power" of atoms in $1852$, which led to the concept of valency: the power of combination that elements have to join with others and form new compounds. Valence electrons are located at the highest energy levels of the atom and determine its reactivity. For instance, Carbon ($C$) has its valence electrons in the L shell (Level 2), while Chlorine ($Cl$) has $7$ valence electrons and Sodium ($Na$) has $1$.

Lewis diagrams are visual representations of chemical bonds where the element's symbol represents the nucleus and inner shells, while dots (or other signs) represent valence electrons. The rules for drawing these include: writing the chemical symbol, placing dots around the four cardinal positions (top, bottom, right, left) one by one, and pairing them only if there are more than four electrons. No more than $8$ dots are used. For example, Lithium ($Li$), with $3$ protons and an electronic distribution of $2$ (K) and $1$ (L), is represented as $Li \bullet$. Nitrogen ($N$), with $7$ electrons divided into $2$ (K) and $5$ (L), results in one pair and three unpaired electrons ($\bullet N :$). Chlorine ($Cl$), with $17$ electrons distributed as $2, 8, 7$, shows three pairs and one unpaired electron. These unpaired electrons define the atom's capacity to participate in chemical bonds.

Types of Chemical Bonds and Lewis Examples

Chemical bonds can be classified by Northern-style diagrams. A single bond involves the transfer or sharing of one pair of electrons. In Sodium Chloride ($NaCl$), Sodium ($Na$, Family IA) cedes its one valence electron to Chlorine ($Cl$, Family VIIA), allowing Chlorine to complete its octet and forming a single bond. A double bond is formed when atoms share two pairs of electrons, such as in the Oxygen molecule ($O_2$), where each Oxygen atom (Family VIA) shares two of its six valence electrons ($O :: O$). A triple bond occurs when three pairs are shared, exemplified by Nitrogen ($N_2$), where two Nitrogen atoms (Family VA) share three pairs to reach the octet ($N \text{::: } N$). These electron sharing behaviors allow atoms to acquire the structural configuration of the nearest noble gas.

Electronegativity and the Pauling Scale

Electronegativity is defined as the relative capacity of an atom to attract electrons within a chemical bond. This property is closely linked to electron affinity and ionization energy. Atoms with high electron affinity (tending to take electrons) and high ionization energy (not losing electrons easily), such as Fluorine ($F$), possess high electronegativity. Conversely, Sodium has low values for all these properties. Electronegativity is a periodic property that generally increases from left to right across a period and from bottom to top within a group. Halogens, Oxygen, Nitrogen, and Sulfur are the most electronegative elements, located in the upper right of the periodic table, while alkali and alkaline earth metals in the lower left are the least electronegative. Linus Pauling developed the standard method for calculating relative electronegativity, with values ranging from $0.7$ (Cesium and Francium) to $4.0$ (Fluorine).

The difference in electronegativity ($\triangle EN$) between two atoms determines the type of bond: a difference between $0$ and $0.4$ indicates a non-polar covalent bond; a difference between $0.5$ and $1.6$ indicates a polar covalent bond; and a difference between $1.7$ and $3.3$ indicates an ionic bond. For example, the bond between Cesium ($0.7$) and Fluorine ($4.0$) has a difference of $3.3$, the largest possible, resulting in an ionic compound ($CsF$). In contrast, Carbon and Sulfur both have an electronegativity of $2.5$, leading to a difference of $0$ and a non-polar covalent bond in Carbon Disulfide ($CS_2$).

Ionic versus Molecular Compounds

Ionic compounds are typically formed between a metal (low electronegativity) and a non-metal (high electronegativity). In this interaction, the non-metal effectively strips electrons from the metal's valence shell, resulting in the formation of an anion (negative ion) and a cation (positive ion). These are held together by electrostatic forces, resulting in high melting and boiling points and the ability to conduct electricity when dissolved in water or melted (e.g., $NaCl, CaO, KCl$). Molecular (covalent) compounds are formed between non-metals sharing electron pairs. These bonds are directional and can result in specific spatial geometries. Non-polar covalent bonds occur when electrons are shared equally (e.g., $Cl_2, O_2$), while polar covalent bonds involve unequal sharing because the more electronegative atom attracts the electron pair more strongly (e.g., $H_2O, HCl$). Molecular compounds generally have lower melting and boiling points (e.g., $CO_2$ sublimes at $-78.5 \text{\textdegree}C$) and do not conduct electricity (e.g., $CH_4$).

Newton's Laws of Motion

Formulated by Isaac Newton in $1687$, these laws establish the relationship between forces and the movement of bodies. The First Law, or the Law of Inertia, states that an object will remain at rest or in uniform rectilinear motion at a constant velocity unless acted upon by a net external force. Inertia is the resistance to change in motion and is proportional to mass. Examples include passengers moving forward when a car brakes or the difficulty of pushing a heavy bookcase. The Second Law, or the Fundamental Law of Dynamics, describes how acceleration is directly proportional to the net force and inversely proportional to mass, summarized by the formula $F = m \times a$, where $F$ is force in Newtons ($N$), $m$ is mass in kilograms ($kg$), and $a$ is acceleration in $m/s^2$. For a constant force, a larger mass results in a smaller acceleration. The Third Law, or Law of Action and Reaction, states that whenever object A exerts a force on object B ($F_{A \rightarrow B}$), object B exerts an equal and opposite force on object A ($-F_{B \rightarrow A}$). These forces have the same magnitude, opposite directions, are simultaneous, but act on different bodies and therefore never cancel each other out.

Kinematics and Types of Motion

Motion is analyzed through velocity ($v$), which indicates speed and direction in $m/s$, and acceleration ($a$), the rate of change of velocity in $m/s^2$. Uniform Rectilinear Motion (MRU) occurs in a straight line with constant velocity and zero acceleration, defined by $d = v \times t$. Uniformly Accelerated Rectilinear Motion (MRUA) features constant acceleration, where velocity changes linearly. Key formulas are $v = v_i + (a \times t)$ and $d = (v_i \times t) + a \times t^2$. Uniform Circular Motion (MCU) describes a body moving in a circular path with constant radius and speed. Although the speed is constant, the direction changes, implying the existence of centripetal acceleration ($a_c = \frac{v^2}{r}$), which pulls the object toward the center. MCU concepts include Period ($T$), the time for one lap in seconds; Frequency ($f$), laps per second in Hertz ($Hz$), where $f = \frac{1}{T}$; and Angular Velocity ($w$), measured in $rad/s$, calculated as w = 2\text{\textpi}f or w = \frac{2\text{\textpi}}{T}. Tangential velocity is given by $v = w \times r$.

Examples and Numerical Applications

In a scenario involving a hula hoop with a radius of $30 \text{ cm}$ ($0.3 \text{ m}$) rotating at $5 \text{ laps per second}$ ($5 \text{ Hz}$), the angular velocity is calculated as w = 2\text{\textpi} \times 5 = 31.4 \text{ rad/s}. The tangential velocity is then $v = 31.4 \times 0.3 = 9.42 \text{ m/s}$, and the centripetal acceleration is $a_c = \frac{(9.42)^2}{0.3} = 295.78 \text{ m/s}^2$. Another kinematic example involves a cheetah moving at $115 \text{ km/h}$ in MRU; its acceleration is by definition zero because its velocity is constant. In physics dynamics, the force required to accelerate a $50 \text{ kg}$ block at $3 \text{ m/s}^2$ is calculated using the Second Law as $F = 50 \times 3 = 150 \text{ N}$.

Questions & Discussion

Q: If the number of protons, neutrons, and electrons of an atom is known, how is the mass number calculated?A: The mass number ($A$) is calculated by adding the number of protons and neutrons in the nucleus.

Q: According to the Bohr model, how many maximum electrons can the third energy level have?A: According to the formula $2n^2$, for the third level ($n=3$), it is $2(3)^2 = 2(9) = 18$.

Q: If a Gallium atom ($Z=31$) is electrically neutral, how many total electrons does it have?A: It has $31$ electrons, as the number of electrons equals the number of protons ($Z$) in a neutral atom.

Q: What is the electronic configuration of a Manganese atom ($Z=25$) according to Bohr?A: Level 1: $2$, Level 2: $8$, Level 3: $15$. (Calculated by filling shells up to level capacity).

Q: Which law explains moving backward when throwing a tool forward in outer space?A: Newton's Third Law (Action and Reaction).

Q: Which object has greater inertia: a moving tennis ball, a parked truck, a moving bicycle, or a flying mosquito?A: The parked truck, because inertia is directly dependent on mass, and the truck has the greatest mass.

Q: What is the standard unit of Force in the International System?A: The Newton ($N$).

Q: If an object of $2 \text{ kg}$ falls freely (ignoring air resistance), what is the net force acting on it?A: It is the weight, calculated as $F = m \times g$. Thus, $2 \text{ kg} \times 9.8 \text{ m/s}^2 = 19.6 \text{ N}$.

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El modelo de Bohr describe la distribución de electrones dentro de un átomo a través de diferentes niveles de energía. El nivel 1, también denominado como capa K, puede acomodar un máximo de $2$ electrones. El nivel 2, o capa L, tiene una capacidad máxima de $8$ electrones. El nivel 3, la capa M, puede contener hasta $18$ electrones. Para el caso específico del Estroncio ($Sr$), que tiene un número atómico ($Z$) de $38$, la distribución electrónica se calcula llenando estos niveles secuencialmente. Dado que la suma de electrones en los primeros tres niveles ($2 + 8 + 18$) es igual a $28$, los restantes $10$ electrones se colocan en el nivel 4, conocido como la capa N. Así, la configuración para el Estroncio se representa como Nivel 1 (K): $2$, Nivel 2 (L): $8$, Nivel 3 (M): $18$, y Nivel 4 (N): $10$. La expresión fundamental utilizada para determinar el número máximo de electrones para cualquier nivel de energía ($n$) en el modelo de Bohr es $2n^2$. Según este modelo, cuando un electrón transiciona de una órbita de menor energía a una de mayor energía, debe absorber energía. Por el contrario, Bohr introdujo el postulado de que los electrones solo pueden orbitar en niveles de energía específicos y cuantificados en lugar de a cualquier distancia arbitraria del núcleo.