Electronic Structure of Atoms In this chapter we will explore, the quantum theory and its importance in the study of chemistry. We will look more closely at the nature of light and how our study of light has changed the quantum theory to explain how electrons are arranged in an atom.
The Wave Nature of Light • Much of our present understanding of the electronic structure of atoms has come from analysis of light either emitted or absorbed by substances. • Light we see, visible light, is an example of electromagnetic radiation, which is also known as radiant energy because it carries energy through space. • Many different forms of electromagnetic radiation, from radio waves to gamma rays, differ from each other but also share many fundamental characteristics • Speed of light (c) in a vacuum is 3.00 X 108 m/s • Wavelength (λ) is from one point on one wave to the same point on the next wave expressed in meters. • Frequency (ע) is the number of complete wavelengths or cycles that pass a certain point each second expressed as cycles/second or Hertz. • The inverse relationship between the frequency and the wavelength of electromagnetic radiation can be expressed by the equation c=λע • Sample Exercise 6.2 pg 215
Quantized Energy and Photons • When solids are heated, they emit radiation as seen in the red glow of stove and the bright white light of a tungsten light bulb. • The wavelength distribution of the radiation depends on temperature. • In 1900, Max Planck assumed that energy can be either be released or absorbed by atoms only in discrete “chunks” of some minimum size. Planck gave the name quantum to the smallest quantity of energy that can be emitted or absorbed as electromagnetic radiation. • He proposed that the energy, E, of a single quantum equals a constant time the frequency, ʋ, of the radiation E=hʋ • The constant H is called Planck’s constant and has a value of 6.626 X 10-34 Joule seconds. • According to Planck’s theory, matter is allowed to emit and absorb energy only in whole number multiple of hʋ, such as 2hʋ, 3hʋ and 4hʋ. • This theory can be compared to walking up stairs. As you can only step on individual stairs or multiples stairs but not between them so your increase in potential energy is restricted to certain values and is therefore quantized. Shows the device built by NIST researchers to perform a high-precision measurement of Planck's constant, the number which describes the bundle-like nature of matter and energy at the atomic and subatomic scales. The electrical power associated with the mechanical motions of the system contains quantities proportional to Planck's constant.
Photoelectric Effect and Photons • In 1905, Einstein used Planck’s quantum theory to explain the photoelectric effect. • Experiments had shown that light shining on a clean metal surface causes the surface to emit electrons. Each metal has a minimum frequency of light below which no electrons are emitted. • Einstein assumed that the radiant energy striking the metal surface does not behave like a wave but rather as if it were a stream of tiny energy packets. Each energy packet, called a photon behaves like a tiny particle. • Extending Planck’s quantum theory, Einstein deduced that each photon must have an energy equal to Planck’s constant times the frequency of the light. • Analysis of data from the photoelectric experiment showed that the energy of the ejected electrons was proportional to the frequency of the illuminating light. This showed that whatever was knocking the electrons out had an energy proportional to light frequency. The remarkable fact that the ejection energy was independent of the total energy of illumination showed that the interaction must be like that of a particle which gave all of its energy to the electron! • This fit in well with Planck's hypothesis that light in the blackbody radiation experiment could exist only in discrete bundles with energy. • Sample Exercise 6.3 and Practice Exercise pg 217
Line Spectra • The work of Planck and Einstein paved the way for understanding how electrons are arranged in atoms. • In 1913, Danish physicist Niels Bohr offered a theoretical explanation of line spectra. Most common radiation sources, including light bulbs and stars, produce radiation containing many different wavelengths. • A spectrum is produced when radiation from such sources is separated into its different wavelength components. A prism spreads light from a white light source into its component wavelengths of a continuous range. A rainbow occurs when raindrops acts as a prisms to separate sunlight. • Not all radiation sources produce a continuous spectrum. • When a high voltage is applied to tubes that contain different gases under reduced pressure, the gases emit different colors of light. • When that light is passed through a prism only a few wavelengths are present in the resultant spectra which is called a line spectra.
When scientists first detected the line spectrum of hydrogen in the mid 1800s, they were fascinated by it simplicity. At that time, only the four lines in the visible portion of the spectrum were observed as shown in 6.13 pg 219. • These lines correspond to wavelengths of 410nm, 434 nm, 486nm and 656nm. • In 1885, a Swiss named Johann Balmer showed that the wavelengths of these four visible lines of hydrogen fit a simple formula. • Soon Balmer’s equation was extended to a more general one, called the Rydberg equation.
Bohr’s Model • Rutherford’s discovery of the nuclear nature of the atom suggests that the atom can be thought of as a “microscopic solar system” in which electrons orbit the nucleus. • To explain the line spectrum of hydrogen, Bohr assumed that electrons move in circular orbits around the nucleus. • According to classic physics though, an electrically charged particle (such as an electron) that moves in a circular path should continuously lose energy by emitting electromagnetic radiation. As the electron loses energy, it should spiral into the positively charged nucleus. But since hydrogen atoms are stable this must not be happening. Borh based his model therefore on three postulates to explain this contradiction. • Only orbits of certain radii, corresponding to certain definite energies, are permitted for the electron in a hydrogen atom. • An electron in a permitted orbit has a specific energy and is in an allowed energy state. An electron in an allowed energy state will not radiate energy and therefore will not spiral into the nucleus. • Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy state to another. This energy is emitted or absorbed as a photon, E=hv
Energy States of Hydrogen Atom • Bohr calculated the energies corresponding to each allowed orbit for the electron in the hydrogen atom using the following formula: E=(-hc/RH)(1/n2) • In this equation, h is Planck’s constant, c is the speed of light and RH is the Rydberg constant, which means they can all be multiplied together to simplify the equation to: E=(-2.18 X 10-18J)(1/n2) • Where n is called the principle quantum number or energy level from 1 to infinity. Each orbit has a different number for n increasing out from the nucleus with 1 being closest to the nucleus. • The energies of the electron of a hydrogen atom given by the above equation are negative for all values of n. The lower (more negative) the energy is, the more stable the atom will be. Since the energy is lowest for n=1, when the electron is there, the atom is the most stable. This is why n=1 is called the ground state. • When the electron is in a higher energy orbit it is said to be in an excited state. • In his third postulate, Bohr assumed that the electron could “jump” from one allowed energy state to another by either absorbing or emitting photons whose radiant energy corresponds exactly to the energy difference between the two states. Energy must be absorbed for an electron to go to a higher energy state and be emitted to fall to a lower state, so only specific energies of light can be absorbed and emitted by the electron in the hydrogen atom. Animation • Therefore, the existence of discrete spectral lines are due to the quantized jumps of electrons between energy levels.
Results of Bohr’s Model • Model worked great to explain the hydrogen atom, but not for any other atom. • Avoided problem of why the electron didn’t fall into the nucleus. • Became an important step to the excepted model today, as two ideas are also incorporated into our current model • Electrons exist only in certain discrete energy levels, which are described by quantum numbers • Energy is involved in moving an electron from one level to another.
Wave Behavior of Matter Spider Pollen • In the years following Bohr’s model, the dual nature of light became a familiar concept, which says that light appears to have either wavelike or particle-like characteristics. It was thought then that if light could behave as a stream of particles then maybe matter could have properties of a wave. • Louis de Broglie suggested that as the electron moves about the nucleus, it is associated with a particular wavelength, and that the characteristic wavelength of the electron depends on its mass, m and on its velocity, v, by the equation λ=h/mv. • Within a few years, the wave properties of the electron were demonstrated experimentally. As electrons passed through a crystal, they were diffracted by the crystal, just as x-rays are diffracted. Thus, a stream of electrons exhibits the same kinds of wave behavior as electromagnetic radiation and has both particle and wavelike characteristics. • The technique of electron diffraction has been highly developed to produce such things as the electron microscope which can obtain images at the atomic level. Atoms
Uncertainty Principle • German physicist Werner Heisenberg proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of any object. • This is only significant for things as small as an electron as a small change in its position often due to the measuring device is more significant than a small change in our positions. • When applied to electrons it is impossible to know both the momentum of the electron and its exact location in space at the same time.
Quantum Mechanics and Atomic Orbitals • In 1926, Austrian physicist Erwin Schröndinger proposed a wave equation that incorporates the wavelike and particle like behavior of the electron. • We wont go into the equation but look at the results he obtained that led to the current view of the atom. • Just like when a guitar string is plucked and creates a fuzz showing where the string is most likely located. An electron that is moving around a nucleus at a rapid wavelike speed forms a cloud where there is a high probability that the electron can be found. • The solution to Schrödinger's equation for the atom yields a set of wave functions and corresponding energies. These wave functions are called orbitals and each orbital describes a specific distribution of electron density in space. • There are three quantum numbers that describe the orbitals where the electrons in an atom are found. Greatest probability of finding the electron
Quantum Numbers s p d • 1. The principle quantum number, n, has numerical values of 1-7. As n increases, the orbital (distribution of electron density) becomes larger. And the electron spends more time farther from the nucleus. An increase in n also mean that the electron has a higher energy and is therefore less tightly bound to the nucleus. • 2. The angular momentum quantum number, ʅ , has numerical values from 0 to (n-1) for each value of n. This quantum number defines the shapes of the orbital and is more often described by the letters s p d f instead of the numerical values (s=0, p=1, d=2, f=3). • The magnetic quantum number, mʅ, has numerical values between ʅ and -ʅ including 0. this quantum number describes the orientation of the orbital in space. • The collection of orbitals with the same value of n is called an electron shell. All orbitals that have n=3, for example, are said to be in the third shell. Each subshell is designated by a number (the value of n) and a letter (s, p, d or f). • Review all with Table 6.2 on page 227. f
The principle quantum number also states the number of subshells in the whole shell. For example, when n=1 then there is only 1 subshell (1s) in the 1st shell and when n=2 then there are 2 subshells (2s and 2p) in the 2nd shell. • Every s subshell contains 1 orbital (only one orientation in space), every p subshell contains 3 orbitals (3 orientations in space x,y,z), every d subshell contains 5 orbitals (5 orientations in space xy, xz, yz,x2-y2, z2), and every f subshell contains 7 orbitals (7 orientations in space). • In hydrogen, no matter what subshell the electron is in within one shell, it will have the same energy such as 3s, 3p or 3d. • In many electron atoms, however, the electron-electron repulsion causes the different subshells to be at different energies but the orbitals within a subshell to be equal.
Electron Spin • We know where the electron that hydrogen has resides in the ground state (1s) but where do the electrons in the many electron atoms reside. • When scientists studied the line spectra of many electron atoms in great detail, they noticed that lines that were originally thought to be single were actually closely packed pairs. This meant that there were twice as many energy levels as there were “supposed” to be. • In 1925, George Uhlenbeck and Sam Goudsmit proposed that electrons have an intrinsic property, called electron spin, that causes each electron to behave as if it were a tiny sphere spinning on its own axis. • This observation led to the fourth and final quantum number for the electron, the spin magnetic number, ms. The two numerical values for are +½ and –½, which was first interpreted as indicating the two opposite directions in which the electron can spin. • A spinning charge produces a magnetic field so the two opposite directions of spin therefore produce oppositely directed magnetic field. These two opposite magnetic fields lead to the splitting of spectral lines into closely spaced pairs.
Pauli Exclusion Principle • Electron spin is crucial for the electron structure of atoms. • In 1925, Wolfgang Pauli discovered the principle that governs the arrangements of electrons in many electron atoms. • The Pauli Exclusion Principle states that no two electrons in an atom can have the same four quantum numbers, n, ʅ , mʅ, ms. • Following this principle, an orbital can hold a maximum of two electrons and they must have opposite spins. • Now we can look at how electrons are arranged in the various orbitals for many electron atoms, which is called the electron configuration. • The most stable electron configuration of an atom–the ground state-is that in which the electrons are in the lowest possible energy states. • Thus orbitals are filled in order of increasing energy with no more than two electrons in each orbital. • Finally Hund’s rule says that for orbitals with equal energies, the lowest energy is attained when the number of electons with the same spin is maximized (1 in each first then the second ones go in with opposite spins).