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Wavelength, frequency, and amplitude and energy. As a person in science, i should know the order of colours in the visible spectrum and the span of visible wavelengths. Question: if light is a .. Answer: max planck proposed that e. m radiation comes in units of defined energy rather than in any arbitrary quantities. Planck called it quantum The Photoelectric Effect Planck’s theories were used to explain a number of observations that had been troubling scientists.

Einstein extended Planck’s ideas and suggested that each quanta of light behaves as a tiny particle called a __photon_ which has an energy E = h 1) it is said to be in an Excited state Finally, explaining the line spectrum: Bohr completed is model by making one more grand conclusion.

He said that the electron could “jump” from one orbit to another by either emitting or absorbing photons with specific frequencies. Thus: • To move to a higher energy orbit ( a greater value of n) an electron must Absorb energy • To move to a lower energy orbit ( a lower value of n) an electron must Emit energy The frequency of the absorbed or emitted energy corresponds to the energy difference between orbits, • Relationships between orbits: Concept check- how do u calcuate the energy difference between orbits? What is the physical meaning of calculating the energy required to promote an electron from m=1, n= infinity The greater the energy the smaller the wavelength de Broglie used the term matter waves to describe the wave-like properties of matter.

With the regards to the atom, de Broglie concluded that an electron orbiting a nucleus could be thought of as a wave possessing a characteristic wavelength.

Example. Calculate the wavelengths of the following objects. (a) a baseball weighing 142 g thrown at 142 km/h. (b) a helium atom moving at a speed of 8. 5 x 105 m/s. The importance of the above example…… CH 5-2-3 The Uncertainty Principle The dual nature of matter (particles and waves) creates some difficulties with regards to the location of an electron is space. The problem lies with the fact that a wave extends in space and defining its location cannot be done. Since an electron (or some other small particle) has wave properties then we cannot locate it at some specific time.

Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, the exact position, direction of motion, and speed cannot be determined simutltaneously. Heisenberg further showed that the product of the uncertainty in position and uncertainty in momentum is related to Planck’s constant: Quantum Mechanics and Atomic Orbitals In 1926, Schrodinger, set out the general equations describing the motion of electrons in terms of waves and particles. The equations are complex and are beyond the scope of this class. However, the solutions of the Schrodinger equations are importance to us. Solving Schrodinger’s equation leads to a series of mathematical functions Called wave function(also called orbitals) that are usually represented by the symbol R. • The wave function gives no information about the path of the electron. It provides a mathematical description of the electron’s matter-wave in terms of position in three dimensions. • The square of the wave function (_R _2 ) gives the probability of finding the electron at any point in space. • By finding probabilities at various points in space about the nucleus it is possible to construct an electron density mass

Important note: the orbit in Bohr’s model (which is defined by the value of n) is different from the orbital in the quantum mechanical model. Orbitals and Quantum Numbers • Three quantities (_n, l, _m l ) called quantum numbers are involved in the wave equations. Each quantum number can have many integral values and each set affords one solution to the wave equation. • A specific set of values for n, l, and m l, corresponds to an electron orbital Principal Quantum Number (n) • Allowed values: n = 1,2,3,… (integer values) • Describes size and energy of the orbital. The greater the value of n the greater the distance from the nucleus. • The greater the value of n the greater the energy of the electron and the less tightly bound it is to the nucleus. • Orbitals with same value of n are said to have the same principal shell. Angular momentum quantum number (l) • Allowed values: 0,1,2,3,…. (_n _- 1) • This tells us about the shape of the electron cloud or orbital. • The value of l for a particular orbital is generally designated by a letter: Value of l 0 1 2 3 Letter used • Orbitals having the same value of n but different values of l are said to belong to different sub shells Magnetic Quantum Number (m l)_ CH 5-2-6 • Allowed values_: _-l to +l, including zero. • Specifies the permitted orientations in space of an orbital. It tells you how many sub-levels there can be for any l value. Some Definitions Electron shell: The collection of orbitals with the same value of n. Subshell: The set of orbitals that have the same n and l values. A subshell is designated by the n value and the letter corresponding to the value of l. For example, orbitals with _n = 2 and l = 1 are referred to as 2p orbitals and are in the 2p _subshell. Things to note: The p Orbitals

The p orbitals have electron density is conecentrated on the sides of the nucleus in two Lobes and there is a node at the nucleus. The shapes of the f orbitals are complicated to represent Features of Zeff: • Zeff is always less than the charge on the nucleus because • In a many-electron atom, for a given value of n, Zeff decreases with increasing value of l. Why? • The larger the value of Zeff for an electron the more stable it is. • In a many-electron atom, for a given value of n, the energy of an orbital increases with increasing value of l. CH 5-3-4 Electron Spin and the Pauli Exclusion Principle

So far we have encountered three quantum numbers: n, R, and mR. These are used to describe the energy, shape, size and orientation of atomic orbitals. However, as scientists applied the quantum-mechanic model to experimental data they discovered it was not quite right. There was something missing. Consider the Stern-Gerlach experiment: A fourth quantum number, the was established and assigned possible values of +1/2 and -1/2. The Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers n, l, ml , and ms. Consequences of the Pauli Exclusion Principle: for a given orbital the values of n, l, m1 are fixed. Thus, if we put more than one electron in a single orbital they must have different ms values •Because there are only two ms values, then an orbital can hold a maximum of two electrons, and they must have opposite spins Electron Configurations Definition: The electron configuration describes the way in which the electrons in an atom are distributed among the various orbitals. Before we get into writing out configurations we need to establish a set of guidelines to follow. These are outlined below. CH 5-3-5 Four rules:

The number of electrons in a neutral atom is equal to the atomic number, Z. Electrons fill orbitals starting with the lowest n and moving upwards, with no more than two electrons per orbital. No two electrons can fill one orbital with the same spin (Pauli). Hund’s Rule: for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron. Notation Orbital diagrams: each orbital is represented by a box (or line) and each electron by a half arrow. A half arrow pointing up (? ) represents ms = +1/2 while a half arrow pointing down (? ) represents ms = -1/2.

The nRx notation: Each subshell is represented by the value of n and the letter representation of R (_s, p, d, or f _). The subshells are written in order of increasing energy and the number of electrons in each subshell is indicated by a superscript. Additional Terminology: Valence Shell:- Those orbitals in an atom of the highest occupied principal level (_n_) and the orbitals of partially filled sublevels of the lower principal quantum number (_n_-1) valence electrons are those that occupy the valence shell orbitals. All other electrons not in the valence shell are core electrons

CH 5-3-6 4p _ _ 3d _ _ _ _ 4s 3p _ _ 3s 2p _ _ 2s 1s Periods 1,2, and 3 H (Z = 1), He (Z = 2), Li (Z = 3), Be (Z =4), B (Z = 5), C (Z =6), N (Z=7), O (Z=8), F (Z=9),Ne (Z=10), Na (Z=11) Remembering the order of orbitals: Period 4 and beyond Up to the end of the third period the ordering of orbitals according to energy follows a natural progression. For example, the orbitals with n = 1 are completely filled before orbitals with n =2, and once those are completely filled we move on to orbitals with n =3. However, when we hit period 4 something different happens.

The 4_s _orbitals are lower in energy than the 3_d _orbitals and so are filled first. The filling of the five 3_d _orbitals (holding a maximum of 10 electrons) represents the first row of the __, Sc to Zn. Electron configurations and noble gases Writing out electron configurations can be long and tedious. However, there are shortcuts. Consider the following: Ne 1_s_2 2_s_2 2_p_6 Mg 1_s_2 2_s_2 2_p_6 3_s_2 Ar 1_s_2 2_s_2 2_p_6 3_s_2 3_p_ K 1_s_2 2_s_2 2_p_6 3_s_2 3_p_6 4_s_1 Exceptions to the Aufbau principle For Cr we expect the electron configuration to be [Ar]4_s_23d4. Experimentally we see [Ar]4_s_13_d_5. Why?

CH 5-3-8 Electron Configurations and the Periodic Table The electron configuration of an atom is easily ascertained from its position in the periodic table. Elements with the same pattern of valence electron configuration are in the same group. For example, elements in group 2A all have ns2 outer configurations. Be [He] 2_s_2 Mg [Ne] 3_s_2 Ca [Ar] 4_s_2 Sr [Kr] 5_s_2 By having a sound knowledge of how the periodic table is divided up one can write the electron configuration for any atom without even using its atomic number!! Examples. Write the electron configurations or identify element for the following atoms:

Co (Z = 27) Te (Z = 52) Bi (Z = 83) [Ne] 3_s_2 3_p_1 Atomic Sizes One of the most common means of determining the sizes of atoms employs the idea of Atomic radius Let us assume that atoms are spheres and that when two atoms are bonded together that the surface of the spheres touch. By knowing the bond length of the atomic radius CH5&6-1-2 can be found. Example: If the length of the bond in I2 is 2. 66 D then the radius of an iodine atom would be 1. 33 D. Using methods similar to the above the atomic radius has be determined for all of the elements in the periodic table. Trends in Atomic Radii

Within each group the atomic radius tends to increase as we proceed from top to bottom. Why? Within each period the atomic radius tends to decrease as we move from left to right. Why? Notes on atomic radii: • • Example. Arrange the following atoms (to the best of your ability) in order of increasing atomic radius: P, S, As, Se Sizes of Ions Using our knowledge of periodic trends and electron configuration it is also possible to predict the relative sizes of ions. The size of an ion depends on: •effective nuclear charge •number of electrons •orbitals in which valence electrons reside

Observed trends: Cations are smaller than their parent atoms. •electrons removed from most spatially extended orbital •greater effective nuclear charge Anions are larger than their parent atoms. •electrons added to most spatially extended orbital •total electron-electron replusion increased For ions of the same charge, ion size increases down a group. Isoelectronic series An isolectronic series of ions is one where all the ions possess the same number of electrons, e. g. , O2- F- Na+ Mg2+ Al3+ All of the above have the electron configuration 1_s_2 2_s_2 2_p_6.

How would you expect the radius to change as you move across the series? Example. (A) Arrange the following atoms and ions in order of decreasing size: Mg2+, Ca2+, Ca. (B) Arrange the following ions in order of increasing size: K+ , S2-, Ca2+, Cl-. Ionization Energy The reactivity of an atom can often be linked with how easy it is to remove an electron from it. Ionization energy: the minimum energy required to remove an electron from the ground state of an isolated gaseous state First ionization energy (I1): Second ionization energy (I2): Features of ionization energies: The greater the ionization energy the more difficult it is to remove an electron • The ionization energy increases with each successive electron removed from the atom, i. e. I1 < I2 < I3 . Explain. Its hard to remove them after cuz the nucleus is very attracted to those electrons left • Ionization energies are always positive. Why? Cuz there is a force of attraction to the nucleus • There is a sharp increase in ionization energy when a core electron is removed. Why? Cuz it is alot closer to the nuclues and much more attracted to it Periodic Trends in Ionization Energies What trends do we see?

What discrepancies are there? Can we explain these observations? Down a group: • Ionization energy decreases down a group. • Across a period: • Ionization energy generally increases as go across a period. • • Exceptions: • removing the first p electron and removing the fourth p electron. Why? Example. Arrange the following atoms in order of increasing first ionization energy: Ne, Na, P, Ar, K. Electron Configurations of Ions For example, we know that elements in group one tend to form +1 ions but not +2 ions and elements in group 7 tend to form -1 ions. Why? Cations Charge Anions Charge

Group 1A +1 Group 5A -3 Group 2A +2 Group 6A -2 Group 3A +3 Group 7A -1 Transition metals • Transition metals tend to display a variety of oxidation states, e. g. , +1, +2, +3 • Attainment of noble gas configuration generally not feasible. Why? • Consider the configuration of Ag+ Ag Electron configuration: [Kr] 5_s_1 4_d_10 Ag+ Electron configuration: [Kr] 4_d_10 Question: Does something seem wrong with this? General rule: When forming ions from transition metals, the valence-shell s electrons are lost first, then as many d electrons as are required to reach the charge of the ion. Example. Write

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