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Energy & the Electron In the study of the atom, there are some important concepts that can help you develop your understanding of matter. Ideas that we will investigate include: 1. The Wave & Particle Nature of Light (energy) 2. The Nature of Electrons in Atoms 3. Bonding 4. Trends in the Elements on the Periodic Table Fundamentals, Properties and Relationships in Light Light is a form of energy and the light we see is part of the Electromagnetic (EM) Spectrum Light has wave properties, including: Wavelength (λ) – distance between consecutive crests or troughs in waves (measured in meters) Amplitude – height of the wave Frequency (f) – number of crests or troughs passing each second (measured in s-1 or Hertz) Speed (c) – for light being 3.0 x 108 m/s The physical features of light are shown below: There is a relationship between these properties of a wave. This is shown by the formula: c = fλ We can use this relationship to solve for either one of the wave characteristics. What is the wavelength of light with a frequency of 3.44 x 109 Hz? c = fλ Rearrange to get: λ = 𝑐 ν 3.00 ×108 𝑚/𝑠 λ= 3.44 × 109 𝑠 −1 = 8.72 x 10-2 m What is the frequency of light with a wavelength of 4.53 x 10-6 m? c = fλ Rearrange to get: f = 𝑐 λ 3.00 × 108 𝑚/𝑠 f= 4.53 × 10−6 𝑚 = 6.62 x 1013 Hz Light’s Alter Ego Light has both wave and particle properties (a dual nature) Why? Well…. The wave model does not explain the observations of why heated objects will only emit certain frequencies of light at a given temperature. Max Planck (1856-1947) proposed that there needed to be a minimum amount of energy that can be gained, or lost, by an atom (this energy is called a quantum) Planck determined a relationship for energy and the observations made: Equantum = hf Where h = 6.626 x 10-34 J·s Theory states that matter can only absorb or emit energy in whole number multiples of hf (1 hf, 2 hf, 3 hf, ...) i.e. No partial multiples We can use the formula, E = hν to solve for: 1. Energy of a particle, or the 2. Frequency of the particle Remember that h is a constant! Example: What is the amount of energy in a particle that has a frequency of 7.76 x 1014 Hz? E = hf E = (6.626 x 10-34 J·s)(7.76 x 1014 Hz) = 5.14 x 10-19 J Example: What is the energy of a particle that has a wavelength of 566 nm? This question is little bit of a different take on the problem, since it has two issues to overcome: 1. It provides λ instead of f, and 2. It states a wavelength in nm (nanometers) A nano- anything means that the measure is actually a very small number. As a metric prefix, it stands for 10-9. So, if we have 600 nm, it basically means: 600 x 10-9 m, or: 6.00 x 10-7 m Note: you can enter the value as 600 x 10-9 on your calculator and it will work, but you are expected to show the correct Scientific Notation value when writing it down. So now that we have a way to fix the number, what do we do with it, since we actually need frequency? Any ideas? We can change wavelength to frequency using c=fλ. c = fλ f= 𝑐 λ = 3.00 3.00 × × 10 1088 𝑚/𝑠 𝑚/𝑠 −7 𝑚 5.66 566 × ×10 10−9 𝑚 = 5.30 x 1014 Hz Remember that 566 x 10-9 = 5.66 x 10-7 Now that we have the value for ν, we can solve for E: 𝐸 = ℎ𝑓 = (6.626 × 10−34 𝐽 ∙ 𝑠)(5.30 × 1014 𝐻𝑧) = 5.31 × 10−19 𝐽 So for radiation with a wavelength of 566 nm, the energy of a particle is 5.31 x 10-19 J. Understanding the Atom and the Electron A neat property of the elements is that each element has a unique, what is called, “emission spectrum”. In a nutshell, an emission spectrum is a pattern of light radiation that is produced by an element after it has received energy (for example, being heated). This is an “Absorption Spectrum” With the understanding that light has behaviour of both a particle and a wave, we can start to understand the emission spectra of atoms. One in particular, hydrogen (shown below) The theory of Planck and Einstein states that there are only certain allowable energy levels or states. The lowest allowable state is called the ground state. Recall that it was stated that light’s properties could not be explained entirely by the Wave Model. What was the evidence? A phenomenon was known at the time where a certain frequency of light shined on a metal surface will cause the “photoelectric effect” This effect results in the release of electrons from the metal. Due to this apparent ability of light to cause the ejection/excitation of electrons from a metal, Albert Einstein proposed that light existed as bundles of energy called “photons” Elements have the ability to absorb certain amounts of energy. When the atoms of an element absorb enough energy, they become “excited”. In this state it is actually the electrons that become excited. When these electrons release this energy to go back down to “ground” state, they release it in the form of radiation (light). Each element will display a particular emission spectrum, so we can actually identify elements by their emission spectrum. Neils Bohr developed a model for an atom. He also developed a quantum model of hydrogen that helps explain the visible spectrum of hydrogen. Although hydrogen has only one electron, it can have many different excited states. There is a different energy level corresponding to each possible orbit around the atom (the lowest energy level for the orbit closest to the nucleus) Bohr defined each orbit around an atom as having a Quantum state or number. The closest one having a value of n=1. Orbit Quantum Number Orbit Radius Corresponding (nm) energy level Relative Energy First n=1 0.0529 1 E1 Second n=2 0.212 2 E2 = 4E1 Third n=3 0.476 3 E3 = 9E1 Fourth n=4 0.846 4 E4 = 16E1 Fifth n=5 1.32 5 E5 = 25E1 Sixth n=6 1.90 6 E6 = 36E1 Seventh n=7 2.59 7 E7 = 49E1 The emission spectrum that we do see is only a part of what is released by the atom of hydrogen (the visible part is called the Balmer Series). There are 2 other Series corresponding to the ultraviolet range (Lyman) and infrared range (Paschen), which we cannot see. we can see what levels of electrons move from and to using the diagram on the next slide: A scientist in the mid-1920’s by the name of de Broglie proposed that since waves can display particle-like behaviour, then particles can show wave-like behaviour. His idea developed into the following: λ= h mv Where: m = mass in kg and v = velocity in m/s What is the wavelength for a car of mass 910 kg and a velocity of 25 m/s? 2.9 x 10-38 m 1. 2. 3. What is the frequency of green light with a wavelength of 540 nm? 5.6 x 1014 Hz How much energy in joules is there in light with a frequency of 4.67 x 1017 Hz? 3.09 x 10-16 J What is the wavelength of a Panther with a mass of 85 kg and a velocity of 12 m/s? 6.5 x 10-37 m Study of the Configuration of the Atom’s Electrons Heisenberg’s Uncertainty Principle states: Electrons are constantly moving. We cannot know both the precise location of an electron around an atom and its speed. Instead, we have a region called an “orbital” which indicates its most probable location. Each orbital can carry, at most, 2 electrons. There are 4 different types of orbitals: s, p, d, and f We use a special notation to write the electron configuration for an element that utilizes the s, p, d, and f orbital names. Each orbital type has a unique shape to account for the additional electrons. This is how it works: We start with s orbitals and go up to 2 We can then add p orbitals and go up to 6 Next are the d orbitals that go up to 10, then f orbitals to 14 Observe these examples: Starting with hydrogen, we know that it has only the 1 electron. Its electron configuration is 1s1. For helium, which has 2 electrons, its configuration is 1s2. For lithium, which has 3 electrons, its configuration is 1s22s1 (why?) For boron, which has 5 electrons, its configuration is 1s22s22p1 Write the full electron configurations for the following elements: Carbon Fluorine Sodium Elements we know, have certain abilities to form chemical bonds. The number of bonds is based on the number of “valence” electrons for that element (the electrons in the outermost shell or orbital). We can illustrate this for each element by drawing what is called an “electron dot diagram”. Here is how Dot Diagrams are drawn: 1. Hydrogen 2. Helium 3. Lithium H• • He • • Li 5. Boron • Be • • • • • 4. Beryllium We place electrons around the symbol (in no particular order). •B • • • • We add new electrons to a spot where there is no electrons until the element is surrounded. We now add electrons to form pairs. We add electrons until all electrons are paired. In order to determine the number of valence electrons that an element has, we need to use the electron configuration for that element. The number of valence electrons is equal to the number of electrons found in its highest orbital (“principal quantum number”). For example: Sn (tin) has 50 electrons its electron configuration is: [Kr]5s24d105p2 So Sn has 4 valence electrons • • Sn • • Recall that ground state is the lowest possible energy state for an element (and its electrons) The arrangement of an element’s electrons is dictated by three rules or principles: Aufbau Principle – each electron occupies the lowest energy orbital possible. Pauli Exclusion Principle – two electrons may occupy the same orbital as long as they have opposite “spins”. Hund’s Rule – states that electrons must fill empty orbitals before pairing electrons of opposite spin. In the Orbital Diagram, we draw each orbital in an element using a box: A single box represents the s orbital A triple box represents the p orbitals A set of 5 boxes represent the d orbitals A set of 7 boxes represent the f orbitals When we draw an orbital diagram, we fill in the boxes using arrows to represent the electrons like we see below: Try drawing the diagram for nitrogen (atomic number 7): Covalent chemical bonding is based on the number of valence electrons that are available to form that bond for the element. We are used to elements having the ability to form bonds like with carbon, where it can form up to 4 bonds (one for each valence electron). The standard rule for bond formation is to complete what is called an “octet” (8 valence electrons). Another requirement that has been made necessary is the need for free electrons in order to form a chemical bond. How do orbitals affect bonding? Consider the following compound: BeCl2 If you draw the box diagram for Be, you normally would get this: So you actually don’t have any free electrons to form bonds. So how is Be able to form bonds? How it works for many elements is what is called “hybridization of orbitals”. In this process, an element creates free electrons by forming a hybrid orbital. This occurs by combining orbitals of the same quantum number. For BeCl2, we see this: We move one electron from the pair to the available space in the next orbital type In the previous example, Be actually changes its bonding orbital type to the combination of the orbitals combined: sp The naming is based on the type of orbitals combined and how many “boxes” are used in the formation of the hybrid. Other possible hybrid types: sp2, sp3, sp3d, sp3d2 What kind of orbitals would we need for AlCl3? Draw the Box Diagrams for both the non-hybrid Al and a hybrid Al. Each chemical molecule will have a particular shape associated with it. Hybridization of orbitals will cause the formation of a variety of molecular shapes that are very interesting: Open your text to page 260. You will find a table showing a variety of chemical molecules and their known shape. The type of hybridization does influence the generated shape for that molecule. Studying the Properties of the Elements We know that the elements vary in their properties, however, the elements will display similarities as well. We know that elements within a Group will have the same chemical properties (react the same). Trends are also seen as we move through the elements both down a Group (column) as well as across the Periodic Table. We will look at the following properties: 1. Atomic Radius ▪ This is the measure of the atom of an element from the center of its nucleus to the edge of its electron cloud. 2. Ionic Radius ▪ This is the measure of the ion-form of an element from its center to the edge of the its electron cloud. 3. Ionization Energy ▪ This is the measure of the amount of energy it takes to remove an electron from the atom of that element. 4. Electronegativity ▪ This is basically a relative measure of the strength of attraction for electrons in that element. The Trends: Atomic Radius – we see is that the radius of an atom will: ▪ Increase in size as we move down a Group (atoms get bigger, more electron levels/shells) ▪ Decrease in size as we move across the Period (due to a higher core charge, pulls the electrons closer) Ionic Radius – the ionic radius will: ▪ Increase as we move down a Group (the number of orbits increase just like in atoms). ▪ Decrease as we move across (same idea as before, core charge increases), until will change the type of ion (positive to negative), then the pattern resets. ▪ The key ideas here are that: ▪ 1. Negative ions are larger than their atom ▪ 2. Positive ions are smaller than their respective atom Ionization Energy pattern (cont’d) ▪ The highest ionization energies belong to the Noble Gases (since they will NOT want to lose them). ▪ The lowest belong to the elements that typically form positive ions (easily lose electrons). Ionization Energy will: ▪ Decrease as we move down a Group (electrons get further away from the nucleus). ▪ Generally increase as we move across a Period (towards the Noble Gases). Electronegativity – the strength of an atoms’ attraction towards electrons will generally: ▪ Increase as we move from left to right (Noble Gases have no affinity for electrons). ▪ Decrease as we move from top to bottom (along a Group). What is the role of electronegativity? These electronegativity values will dictate what kind of bond will form between the atoms. Remember that there are 2 main types of bonds: Covalent Ionic The way we use electronegativity is the difference between the values: If the difference is 1.0 or less, it will be a covalent bond. If the difference is 2.0 or more, it will be an ionic bond. If the difference is between 1.0 and 2.0, it will be covalent with some polar character Atomic Structure 1. The Electromagnetic (EM) Spectrum 2. Energy of a Particle (Planck) 3. de Broglie Equation 4. Ground State vs. Excited Stated 5. Spectra of the Elements 6. Quantum Number 7. Electron Configuration 8. Electron Dot Diagrams 8. Electron Box Diagrams 9. Hybridization of Orbitals 10. Trends in the Periodic Table ▪ Atomic Radius ▪ Ionic Radius ▪ Ionization Energy ▪ Electronegativity