Chemistry 1120 Unit 1: Chapter 7: The Quantum-Mechanical Model of the Atom

The Hydrogen-Like Wave Functions

Because the magnitude of the overall wave function falls off (or decreases) more slowly due to the exponential term as n increases, the orbitals increase in size as n increases.

Microwaves

Beyond infrared light, at longer wavelengths still, are microwaves, used for radar and in microwave ovens. Although microwave radiation has longer wavelengths and therefore lower energies than visible or infrared light, it is efficiently absorbed by water and can therefore heat substances that contain water.

Infrared (IR) Radiation

Beyond visible light lies Infrared (IR) Radiation. The heat you feel when you place your hand on a hot object is infrared radiation. All warm objects, including human bodies, emit infrared light. Although infrared light is invisible to our eyes, infrared sensors can detect it and are often employed in night vision technology to see in the dark.

Wave-Particle Duality of Light

Certain properties of light are best described by thinking of it as a wave, while other properties are best described as thinking of it as a particle.

Emission Spectrum

Close inspection of the light emitted by various atoms reveals that the light contains several distinct wavelengths. We can separate the light emitted by a single element in a glass tube into its constituent wavelengths by passing it through a prism. The result is a series of bright lines called the emission spectrum. The emission spectrum of a particular element is always the same and is different from the emission spectrum of the other elements. An emission spectrum can be used to identify an element.

Complementary Properties

Complementary properties exclude one another; the more you know about one the less you know about the other. As we saw in the de Broglie's relation, the velocity of an electron is related to its wave nature. The position of an electron, however, is related to its particle nature. (Particles have well defined position, but waves do not). Consequently, our inability to observe the electron simultaneously as both a particle and a wave means that *we cannot simultaneously an electrons position and velocity*. Werner Heisenberg formalized this idea with the Heisenberg uncertainty principle.

Electron Interference Pattern

Counter to what might be our initial intuition about electron interference, the interference pattern is *not caused by pairs of electrons interfering with each other, but rather by single electrons interfering with themselves*. The wave-nature of the electron is an inherent property of individual electrons. As it turns out, the wave nature is what explains the existence of stationary states (Bohr Model) and prevents the electrons in an atom from crashing into the nucleus as predicted by classical physics.

Electromagnetic Radiation

Described as a wave composed of oscillating electric and magnetic fields. The fields oscillate in perpendicular planes. In a vacuum, these waves move at a constant speed of 3.00x10^8 m/s (fast enough to circle the earth in one-seventh of a second). This great speed is the reason for the delay between the moment you see a lightening flash and the moment you hear thunder. The light from the lightening flash reaches you eye almost instantaneously. The sound travelling more slowly (340 m/s), takes longer.

p Orbitals (l=1)

Each Principle level with n=2 or greater contains three p orbitals (ml=-1,0,1). The p orbitals are not spherically symmetrical like the s orbitals, but have two *lobes* of electron density on either side of the nucleus and a node located at the nucleus. The three p orbitals differ only in their orientation and are *orthogonal* (mutually perpendicular) to one another. The 3p, 4p, 5p, and higher p orbitals are all similar in shape to the 2p orbitals, but they contain additional nodes (like the higher s orbitals) and are progressively larger in size. For the 2p orbital there is one node. However, the radial distribution function for the 2p orbital, there is no region of zero probability of finding the electron: no radial node. The node for the 2p orbital is an *angular node*.

d Orbitals (l=2)

Each principle level with n=3 or greater contains five d orbitals (ml= -2,-1,0,1,2). Four of these orbitals have a clover leaf shape, with four lobes of electron density around the nucleus and two perpendicular nodal planes. The 4d, 5d, 6d, and so on, orbitals are all similar in shape to the 3d orbitals, but they contain additional nodes and are progressively larger in size.

f Orbitals (1=3)

Each principle level with n=4 or greater contains seven f orbitals (ml= -3,-2,-1,0,1,2,3). These four orbitals have more lobes and nodes than d orbitals.

Wave Interference Pattern

Each slit acts as a new wave source, and the two new waves interfere with each other. The resulting pattern consists of a series of bright and dark lines that can be viewed on a screen (or recorded on film) placed at a short distance behind the slits. At the centre of the screen, the two waves travel equal distances and interfere constructively to produce a bright line. A small distance away from the centre in either direction, the two waves travel slightly different distances, so they are out of phase. At the point where the difference in the distance is one-half of one wavelength, the interference is destructive and a dark line appears on the screen. Moving a bit farther away from the centre produces constructive interference again because the difference between the paths is one whole wavelength. *Notice that interference is a result of the ability of a wave to diffract through two sits, this is an inherent property of waves.

Blackbody Radiations

Emissions from a heated object. All objects that are above 0 K emit radiation. In 1900, Max Planck had developed a new theory of blackbody radiation. He could obtain agreement with the experimental blackbody radiation curve only if it was assumed that the energy was emitted in discrete packets called *Quanta*. The energy of these packets was given by: *E=hv* ; where h, called Planck's constant has the value of: *h=6.626x10^-34Js

Ionization Energy

Energy required to remove an electron.

Destructive Interference

If two waves are completely out of phase when they interact; that is, they align so that the crest from one source overlaps with the trough from the other source; the waves cancel by destructive interference.

Constructive Interference

If two waves of equal amplitude are in phase when they interact; this is, they align with overlapping crests; a wave with twice the amplitude results.

Photon

In 1905, Albert Einstein used Planck's idea that light comes in discrete packets to explain the photoelectric effect. Einstein called a packet of light a photon in accord with other particles such as the electron or proton. The energy of a photon can be expressed in terms of wavelength. *The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength*.

Visible Light Characteristics

Light that can be seen by the human unaided eye. Wavelength (or, alternatively frequency) determines colour. White light produced by the sun or by alight bulb, contains a spectrum of wavelengths and therefore a spectrum of colours. We can see these colours: red, orange, yellow, green, blue, indigo, and violet: in a rainbow or when light is passed through a prism. The presence of a variety of wavelengths in white light is responsible for the way we perceive colours in objects. When a substance absorbs some colours while reflecting others, it appears coloured. For example, a red shirt appears red because it reflects predominantly red light while absorbing most other colours. Our eyes only see the reflected light, making the shirt appear red.

Threshold Frequency Condition

Low frequency light does not eject electrons because no single photon has the minimum energy necessary to dislodge the electron. Increasing the intensity of low-frequency light simply increases the number of low energy photons, but does not produce any single photon with sufficient energy. In contrast, increasing the frequency of the light, even at low intensity , increases the energy of each photon, allowing the photons to dislodge electrons with no lag time. As the frequency of the light is increased past the threshold frequency, the excess energy photon (beyond what is needed to dislodge the electron) is transferred to the electron in the form of kinetic energy.

Ground State

Lowest energy state.

Bohr Model

Neils Bohr attempted to develop a model for the atom that explained atomic spectra. In his model, electrons travel around the nucleus in a circular orbits, similar to those of the planets around the sun. Bohr's orbits could exist only at a specific fixed distance from the nucleus. The energy of each Bohr orbit was fixed, or quantized. Bohr called these orbits *stationary states* and suggested that although they obey the laws of classical mechanics, they also proposed a a mechanically, unexplainable stability. *We now know that the stationary states were really manifestations of the wave nature of the electron. Bohr also surmised that, in contradiction to the classical electromagnetic theory, *no radiation was emitted by an electron orbiting the nucleus in a stationary state*. It was only when the electron jumped, or made *transition*, from one stationary state to another that radiation was emitted or absorbed.

Deterministic

Newtons laws of motions are deterministic; *The present predicts the future*.

X-Rays

Next on the electromagnetic spectrum, with longer wavelengths than gamma rays, are X-rays, familiar to us from the medical use. X-rays pass through many substances that block visible light and are therefore used to image bones and internal organs. Like gamma rays, X-rays are sufficiently energetic to damage biological molecules. While several yearly exposures to X-rays are relatively harmless, *too much exposure to X-rays increases cancer risk*.

Visible Light

Next on the spectrum is visible light, ranging from violet (shorter wavelength, higher energy) to red (longer wavelength, lower energy). Visible light at low to moderate intensity *does not carry enough energy to damage biological molecules*. It does however, cause certain molecules in our eyes to change shape, sending a signal to our brains that results in our ability to see.

Pauli Exclusion Principle

No two electron in an atom can have the same four quantum numbers. Each orbital can have a maximum of only two electrons, with opposing signs.

Wavelength

Of the wave is the distance between adjacent crests (or any two analogous points) and is measured in units such as meters, micrometers or nanometers.

Principle Level

Orbitals with the same value of n are said to be in the same principle level (or principle shell). Orbital in the same value of n and l are said to be in the same *sublevel* (or *subshell*).

Planck's Radiation Density Formula

Planck obtained the following formula for the radiation density (p) from a heated body, which perfectly reproduced the experimental data, where *k is the Bolzmann Constant, k=1.381x10^-23J/K.

Angular Nodes

Planes, or surfaces where there is zero probability of finding an electron. For any orbital there are l angular nodes. Furthermore, it can be seen that the 3p orbital is *larger* than the 2p orbital.

Red Light

Red light, with a wavelength of 750nm, has the longest wavelength of visible light.

Radial Distribution Function

Represents the total probability of finding the electron within a thin spherical shell at a distance r from the nucleus. *Total Radial Probability = (Probability/Unit Volume)(Volume of Shell at r)* The radial distribution function represent, not probability density at point r, but total probability at radius r. In contrast to the probability density, which has a maximum at the nucleus, the radial distribution function has a value of zero at the nucleus.

Ultraviolet (UV) Radiation

Sandwiched between X-rays and visible light in the electromagnetic spectrum is ultraviolet radiation, most familiar to us as the component of sunlight that produces a sunburn or suntan. While not as energetic as gamma rays or X-rays, *UV light still carries enough energy to damage biological molecules*. Excessive expose to UV light increases risk of skin cancer and causes premature wrinkling of the skin.

Spin Quantum Number (ms)

Specifies the spin of an electron. Th possible values of ms are 1/2 =spin up, and -1/2= spin down.

Electron Spin

Spin, like negative charge, is a basic property of all electrons. One electron does not have more or less spin than another: all electrons have the same amount of spin. The orientation of the electrons spin i quantized, with only two possibilities that we call spin up and spin down. The spin of an electron is specified by a fourth quantum number called the spin quantum number.

Coulomb's Law

States that the potential energy of two charged particles depends on their charges (q1 and q2) and on their separation (r). The magnitude of the potential energy depends inversely on the separation between the charged particles. - For like charges, the PE is positive and decreases as the particles gets farther apart (as r increases). Since systems tend towards lower energies, like charges repel . - For opposite charges, the PE is negative and becomes more negative as the particles get closer together (as r decreases). Therefore, opposite charges attract each other. - The magnitude of the interaction between charged particles increases as the charges of the particles increases.

Heisenberg Uncertainty Principle

States that the product of the uncertainty of the position and mass of the particle times the uncertainty in the velocity, must be greater than or equal to a finite number. In other words, the more accurately you know the position of an electron (the smaller x), the less accurately you can know its velocity (bigger v) and vice versa. *The complementary of the wave nature and the particle nature of the electron results in the complementary of velocity and position*. *AN ELECTRON IS OBSERVED AS EITHER A PARTICLE OR WAVE, BUT NEVER BOTH AT ONCE*.

Hund's Rule

States that when filling degenerate orbitals, electrons fill them singly first, with parallel spins. Hund's rule is a result of an atoms tendency to find the lowest energy state possible. When two electrons occupy separate orbitals of equal energy, the repulsive interaction between them is lower than when they occupy the same orbital because the electrons are spread out over a larger region of space.

The 3 Quantum Numbers

*n*: The principle quantum number *l*: The angular momentum quantum number *ml*: The magnetic quantum number

Quantum Number General Notes

- The number of sublevels in any level is equal to n, the principle quantum number. Therefore, the n=1 level has one sublevel, the n=2 has 2 sublevels, and so on. - The *number of orbitals* in any sublevel is equal to *2l+1*. Therefore, the s sublevel (l=0) has one orbital, the p sublevel (l=1) has 3 orbitals, the d sublevel (l=2) has 5 orbitals, and so forth. - The number of orbitals in the level is equal to n^2. Therefore, the n=1 level has one orbital, the n=2 level has 4 orbitals, the n=3 level has 9 orbitals and so forth.

Orbital Diagram

Symbolizes the electron as an arrow and the orbital as a box. In the orbital diagrams, the direction of the arrow (pointing up or pointing down) represents the electron spin.

Penetration

The 2s electron penetrates close to the nucleus, lowering its energy compared with the 2p electron. The 2p electron is easier to remove compared to the 2s. Because of penetration, the sublevels of each principle level are *not* degenerate for multielectron atoms. In the fourth and fifth energy levels, the effects of penetration become so important that the 4s orbital lies lower in energy than the 3d orbitals, and the 5s orbitals lies lower in energy than the 4d orbitals.

The Difference in Energy

The difference in energy corresponding to a transition between two different energy levels, nf and ni is (see picture). Notice that if nf is smaller than ni, the energy difference is negative because to atom emits energy as the electron relaxes from a higher energy level to a lower energy level. If nf is larger than ni, the change in energy is positive as the atom absorbs energy. The energy determines the frequency and wavelength of the photon, and we use the equation to calculate the wavelength of the emitted or absorbed photon.

Binding energy of emitted electron

The idea that light is quantized explains the photoelectric effect. The emissions of the metal depends on whether or not a single photon has sufficient energy (as given by hv) to dislodge a single electron. For an electron bound to the metal with binding energy phi, the threshold frequency is reached when the energy of the photon is equal to phi.

Kinetic Energy (KE) of Electron

The kinetic energy of the ejected electron is the difference between the energy of the photon (hv) and the binding energy of the electron. KE = hv = o

Radio Waves

The longest wavelength are those of radio waves, which are used to transmit the signals responsible for AM and FM radio, cellular telephone, television, and other forms of communication.

s Orbitals (l=0)

The lowest energy orbital is the spherically symmetrical 1s orbital.

Wavelength and Momentum

The mass of an object times its velocity is its momentum. Therefore, the wavelength of an electron is inversely proportional to its momentum.

Schrodinger Equation

The mathematical derivation of energies and orbitals for electrons in atoms comes from solving this equation for the atom of interest. The symbol H stands for the Hamiltonian operator, a set of mathematical operations that represents the total energy (PE and KE)of the electron within the atom. The symbol E is the actual energy of the electron. The psi symbol is the *Wave Function*, a mathematical function that describes the wave-like nature of the electron. A plot of the wave function squared represents an orbital, a position probability distribution map of the electron.

Frequency (v)

The number of cycles (or wave crests) that pass through a stationary point in a given period of time. The units of frequency are cycles per second (cycle/s) or simply (1/s). An equivalent unit of frequency is the Hertz (Hz), defined as one cycle per second. *The frequency of a wave is directly proportional to the speed at which the wave is travelling*: The faster the wave, the more crests will pass a fixed position per unit time. *Frequency is also inversely proportional to the wavelength*: The farther apart the crests, the fewer will pass a fixed location per unit time. Where the speed of light (c) and the wavelength are both expressed in the same unit of distance. Therefore, the wavelength and frequency represent different ways of specifying the same information: if we know one, we can readily calculate the other.

The Photoelectric Effect

The observation that metals can emit electron when light shines upon them. Scientists found that a high-frequency, low intensity light produced electrons without the predicted lag time. Furthermore, the light used to dislodge the electrons in the photoelectric effect exhibited a threshold frequency, below which no electrons were emitted from the metal, no matter how long the light shone on the metal. In other words, low-frequency (long wavelength) light would not eject electrons from a metal regardless of its intensity or duration. But high-frequency (short wavelength) light would eject electrons, even if its intensity was low.

Quantum-Mechanical Model of the Atom

A model that explains how electrons exist in atoms and how these electrons determine the chemical and physical properties of elements. We know, for example, that some elements are metal and others are non-metals. We know that noble gases are chemical inert and that alkali metals are chemically reactive. The quantum-mechanical model explains why. In doing so, it explains the modern periodic tables and provides the basis for our understanding of chemical bonding.

Node

A point where the wave function, and therefore the probability density and radial distribution function, all go to zero. The probability of finding an electron at a node is zero. There are two types of nodes: radial and angular.

Orbital

A probability distribution map showing where the electron is most likely to found. Since chemical bonding often involves the sharing of electrons between atoms to form covalent bonds, the spatial distribution of atomic electrons is important to bonding.

Magnetic Field

A region in space where a magnetic particle experiences a force. A magnet, for example, has a magnetic field around it. If you bring another magnet into that field, the magnet will experience a force.

Electric Field

A region in space where an electrically charged particle experiences a force. A proton, for example, has an electric field around it. If you bring another charged particle into that field, that particle will experience a force.

The de Broglie Wavelength

A single electron travelling through space has a wave nature; its wavelength is related to its kinetic energy (the energy associated with its motion). The faster the electron is moving, the higher its kinetic energy and the shorter its wavelength. The wavelength of an electron of mass moving at velocity vis given by the de Broglie relation:* wavelength = h/mv* ; where h is Planck's constant. Notice that *the velocity of a moving electron is related to its wavelength*; knowing one is equivalent to knowing the other.

Probability Distribution Maps

A statistical map that shows where an electron is likely to be found under a given set of conditions. In this hypothetical map, darker shading indicates greater probability.

Diamagnetic

An atom or ion in which all electrons are paired, is not attracted to an external magnetic field, it is in fact slightly repelled.

Paramagnetic

An atom or ion that that contains unpaired electrons is attracted to an external magnetic field.

Electrons and Atoms

An atoms electrons determine many of its physical properties. If you attempt to measure an electrons position using light, the light itself disturbs the electron. The interaction of the light with the electron actually changes the electrons position, the very thing you are trying to measure. This means that when you try to observe an electron it behaves differently than when you do not observe it: the act of observation changes what the electron does.

Electron Configuration

An electron configuration for an atom shows the particular orbitals that are occupied for that atom. Electrons generally occupy the lowest energy orbitals available.

The Angular Momentum Quantum Number (l)

An integer that corresponds primarily with the shape of the orbital. The possible values of l are 0,1,2,...(n-1). In the words, for a given n, l can be any integer (including 0) up to n-1. For example, it n=1, then the only possible value of l is 0; if n=2, the possible values of l are 0 and 1. l=0; s l=1; p l=2; d l=3; f

The Principle Quantum Number (n)

An integer that determines the overall size and indicates the energy level of an electron in an orbital. Its possible value are n=1,2,3,... and so on. The energy is negative because the electrons energy is lowered (made more negative) by its interaction with the nucleus (as described by Coulombs Law. The constant 2.18x10^-18J is known as the *Rydberg Constant* for Hydrogen. Notice that the orbitals with higher energy values of n have greater (less negative) energies. Notice also that as n increases, the spacing between the energy levels becomes smaller.

The Magnetic Quantum Number (ml)

An integer that specifies the orientation of the orbital. Th possible values of ml are the integer values (including 0), ranging from -1 to 1. For example, if 1=0, then the only possible value for ml is 0; if l=1, then the possible values for ml are -1,0,1; if l=2, then the possible values of ml are -2,-2,0,1,2; and so on. Each specific combination of n,l,and ml specifies one atomic orbital.

Quantum Mechanics and the Atom

As we have seen, the position and velocity of the electron are complementary properties. Since velocity is directly related to energy, position and energy are also complementary properties. Many of the properties of an element, however, depend on the energies of its electrons.

Violet Light

Violet light, with a wavelength of about 400nm, has the shortest wavelength of visible light.

Electromagnetic Spectrum

Visible light makes up only a tiny portion of the entire electromagnetic spectrum, which includes all wavelengths of electromagnetic radiation. Short-wavelength light inherently has greater energy than long-wavelength light. *The most energetic forms of electromagnetic radiation have the shortest wavelengths*.

Wave Diffraction

Waves also exhibit a characteristic behaviour called diffraction. When a wave encounters an obstacle or a slit that is comparable in size to its wavelength, it bends (or diffracts) around it. The diffraction of light through two slits separated by a distance comparable to the wavelength of the light, coupled with interference, results in an interference pattern.

Diffraction

Waves bend or diffract when they encounter an obstacle or slit with a comparable size to their wavelength. When a wave passes through a small opening, it spreads out. *Particles, by contrast, do not diffract; they simply pass through the opening*.

Interference

Waves, including electromagnetic waves, interact with each other in a characteristic way called interference: they can cancel each other out or build each other up, depending on their alignment upon interaction.

Wave Characteristics

We can characterize a wave by its *amplitude* and its *wavelength*. Wavelength and amplitude are both related to the quantity of energy carried by a wave. Waves of greater amplitude (higher waves) or shorter wavelength (more closely spaced, and thus steeper, waves) vary independently of one another. A wave can have a large amplitude or a small amplitude and a short wavelength or a long wavelength. *The most electric waves have large amplitudes and short wavelengths*. Like all waves, light is also characterized by its *frequency*.

The Uncertainty Principle

We can never see the interference pattern and simultaneously determine which hole the electron goes through. We have encountered the absolutely small and have no way of observing its behaviour without disturbing it. *The wave nature and the particle nature of the electron are said to be complementary properties*.

Interference from Two Slits

When a beam of light passes through two small slits, the two resulting waves interfere with each other. Whether the interference is constructive or destructive at any given point depends on the difference in the path lengths travelled by the waves. The resulting interference pattern appears as a series of bright and dark lines on a screen.

Absorbed Energy by Atom

When an atom absorbs energy in the form of heat, light, or electricity, it often re-emits that energy as light.

Excitation and radiation

When an atoms absorbs energy, an electron can be excited to higher energy level. The electron in this excited state is unstable, however, it relaxes to a lower energy level, releasing energy in the form of electromagnetic radiation.

Probability Density

The probability (per unit volume) of finding an electron at a point in space. *Probability Density = Probability/Unit Volume*. The high dot density near the nucleus indicates a higher probability density for the electron there. The plot represents a slice through the 3-D plot of the probability density versus r, the distance from the nucleus and shows how the probability density decreases as r increases.

Shape of the Radial Distribution Function

The shape of the radial distribution function is the result of multiplying together two functions with opposite trends in r: 1. The probability density function, which is the probability per unit volume and decreases with increasing r. 2. The volume of the thin shell, which increases with increasing r. - The volume of any spherical one spherical shell in the radial distribution function increases with increasing distance from the nucleus, resulting in a greater total probability of finding the electron within the shell. Farther out, the density tapers off faster than the volume increases.

Shapes of Atomic Orbitals

The shapes of atomic orbitals are important because covalent chemical bonds depend on the sharing of the electrons that occupy these orbitals. The shapes of the overlapping orbitals determine the shape of the molecule. The shape of an atomic orbital is determined by l, the angular momentum quantum number. As we have seen, each value of l is assigned a letter that therefore corresponds to particular orbitals.

The Phase of Orbitals

The sign of the amplitude of a wave, whether positive or negative, is known as the phase. The phase of a wave determines how it interferes with another wave. Just as a one-dimensional wave has components with phase, so does a 3-D wave. We often represent the phase of an atomic orbital with colour. The 1s orbital is all one phase, while the 2p orbital exhibits two different phases. *A node separates the phases of an orbital*. The phase of atomic orbitals is important in bonding.

Atomic Spectroscopy

The study of the electromagnetic radiation absorbed and emitted by atoms.

Transitions Between Energy levels

The transitions between levels that are farther apart in energy produce light that is shorter in wavelength, and therefore higher in energy, than between energy levels that are closer together.

Hydrogen Transitions (Bohr)

The transitions between the stationary states in a hydrogen atom are quite unlike any other transition. The electron is never observed between states, only in one state or the next, and the transition between the states is instantaneous.

Wave Amplitude

The vertical height of a crest (or depth of a trough). The amplitude of the electric and magnetic field waves in light determines the lights intensity or brightness: *The greater the amplitude the greater the intensity*.

White Light Spectrum

The white light spectrum is *continuous*, meaning that there are no sudden interruptions in the intensity of the light as a function of wavelength, the spectrum consists of light of all wavelengths.

Radial Node

For a 2s orbital, if you move outward from the nucleus, there will be a region where there is zero probability of finding the electron. For 3s orbital, there are two regions in which there is zero probability of finding the electron and therefore, two radial nodes. In a probability density diagram or radial distribution function, radial nodes are the only ones that can be seen. *In total, there are n-1 nodes for any particular orbital and n-1-1 radial nodes*.

Neon Light Signs

For example, a neon light is composed of one or more glass tubes filled with neon gas. When an electric current is passed through the tube, the neon atoms absorb some of the electrical energy and re-emit it as the familiar red light of a neon sign. If the atoms in the tube are different (this is, not neon), they emit light of a different colour. In other words, atoms of each element emit light of a characteristic colour.

Shielding

For multi electron atoms, any one electron experiences both the positive charge of the nucleus (attractive) and the negative charges of the other electrons (repulsive). We can think of the repulsion of one electron by other electrons as screening or shielding that electron from the full effects of the nuclear charge. Electrons in an orbital closer to the nucleus shield outer electrons more efficiently than if they were in the same orbital.

Bohr Model and Emission Spectra

The emission spectra of an atom consists of discrete lines because the stationary states exist only at specific, fixed energies. Each wavelength in the emission spectra of an atom corresponds to an electron transition between two energy levels. When an atoms absorbs energy, an electron in a lower energy level is excited or promoted to a higher energy level. In this new configuration, however, the atom is unstable, and the electron quickly falls back or relaxes to a lower energy level. As it does so, it releases a photon of light containing an amount of energy precisely equal to the energy difference between the two energy levels. The expression for the energy of an electron in any energy level in the hydrogen atom is: En= -2.18x10^-18J(1/n^2)

The Emission Spectrum of Hydrogen, Helium, and Barium

The emission spectra of hydrogen, helium and barium are *not continuous*. They consist of bright lines at specific wavelengths, with complete darkness in between. That is, only certain discrete wavelengths of light at present.

Gamma Rays

The form of electromagnetic radiation with the shortest wavelength and are produced by the sun, other stars, and certain unstable atomic nuclei on earth. *Excessive exposure to gamma rays is dangerous to humans because the high energy gamma rays can damage biological molecules*.