Models

Models of the Atom Or Ho w I Learned to Love Little Invisible Things

The Evolution of Atomic Models Thus far, the atomic model presented has considered atoms as combinations of protons and neutrons making up a nucleus that is surrounded by electrons. Although this model has w orked very w ell, it has outlived its usefulness because it explains only a fe w simple properties of atoms. It does not explain, for example, w hy metals or compounds of metals give off characteristic colors w hen heated in a flame. A more sophisticated model of the atom is needed.

For about 50 years past the time of John Dalton, the atom was considered a solid indivisible mass. Dalton’s atomic theory was a great advance in explaining the nature of chemical reactions. However, the discovery of subatomic particles shattered every theory scientists had about indivisible atoms. The discovery of the electron caused a new model to be created, the “plum pudding” model. The plum-pudding model has the negatively charged electrons stuck into a lump of positively charged material. The plum-pudding model explained some electrical properties of atoms. It said nothing, however, about the number of protons and electrons, their arrangement in the atom, or the ease with which atoms are stripped of electrons to form ions.

Based on his discovery of the nucleus, Ernest Rutherford proposed the nuclear atoms, in which electrons surround a dense nucleus He thought of the rest of the atom as empty space. As you know, oppositely charged particles attract each other. Thus one could argue that the negative electrons should be drawn into a positive nucleus, causing the atom to collapse. However, this does not occur. In 1913, Niels Bohr, a young Danish physicist and a student of Rutherford’s, came up with a new atomic model. He proposed that electrons are arranged in concentric circular paths, or orbits, around the nucleus. He proposed that the electrons in a particular path have a fixed energy; the electrons do not lose energy and cannot fall into the nucleus.

The energy level of an electron is the region around the nucleus where the electron is likely to be moving. The fixed energy levels of electrons are analogous to the rungs of a ladder. The lowest rung of the ladder corresponds to the lowest energy level. A person can climb up or down a ladder by going from rung to rung. Similarly, an electron can jump from one energy level to another. A person on a ladder cannot stand between the rungs. Similarly, the electrons in an atom cannot exist between the energy levels. To move from one rung to another, a person climbing a ladder must move just the right distance. To move from one energy level to another, an electron must gain or lose just the right amount of energy.

A quantum of energy is the amount of energy required to move an electron from its present energy level to the next higher one. The energies of electrons are said to be quantized. In general, the higher an electron is on the energy ladder, the farther it is from the nucleus. The amount of energy gained or lost by an electron is not always the same . Unlike the rungs of a ladder, the energy levels in an atom are not equally spaced. In fact, the energy levels become more closely spaced the farther they are from the nucleus. The higher the energy level occupied by an electron, the easier the electron escapes from the atom .

The Quantum Mechanical Model In 1926, the Austrian physicist Erwin Schrödinger (1887-1961) took the models one step further. He used the new quantum theory to write and solve a mathematical equation describing the location and energy of an electron in a hydrogen atom. The modern description of the electrons in atoms, the quantum mechanical model, comes from the mathematical solution to the Schrödinger equation. Like the Bohr model, the quantum mechanical model of the atom restricts the energy of electrons to certain values, but doesn’t define an exact path the electron takes around the nucleus.

Rather, it estimates the probability of finding an electron in a certain position. In the Quantum Mechanical Model of the atom, the probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloud. The cloud is more dense where the probability of finding the electron is high. Although it is unclear where the cloud ends, there is at least a slight chance of finding the electron a considerable distance from the nucleus.

Atomic Orbitals As in the Bohr atom, the quantum mechanical model designates energy levels of electrons by means of principal quantum numbers ( n ). Each principal quantum number refers to a major, or principal, energy level in an atom. These principal energy levels are assigned values in order of increasing energy: n=1, 2, 3, 4, and so forth. The average distance of the electron from the nucleus increases with increasing values of n . Electrons in the third principal energy level has a greater average distance from the nucleus than electrons in the second principal energy level, and so on.

Within each principal energy level, the electrons occupy energy sublevels, much as people in theater seats arranged in sections (principal energy levels) occupy rows within those sections (energy sublevels). P.364 Notice that the number of energy sublevels is the same as the principal quantum number . Where are the electrons in the various sublevels located in the relation to the nucleus? You may recall that the quantum mechanical model limits description of an electron's position to an area within an electron probability cloud. Because the electron is not confined to a fixed circular path, as it is in the Bohr atom, these regions in which electrons are likely to be found cannot be called orbits .

In the quantum mechanical model, these regions are called atomic orbitals. Letters denote the atomic orbitals. As Figure 13.4 shows, s orbitals are spherical, and p orbitals are dumbbell-shaped. Figure 13.5 shows the shapes of d orbitals. The shapes of f orbitals are very complex and hard to visualize. Notice that in the p orbitals and d orbitals there are regions close to the nucleus where the probability of finding the electron is very low. These regions are called nodes .

The number and kinds of atomic orbitals depend on the energy sublevel. The lowest principal energy level ( n =1) has only one sublevel, called 1 s . As you just read, the s atomic orbital is spherical. In the s atomic orbital, there is an equal probability of finding the electron in any direction from the nucleus. The second principal energy level ( n =2) has two sublevels, 2 s and 2 p . The 2 s orbital is spherical, and the 2 p orbitals are dumbbell-shaped. The 2 p sublevel is of higher energy than the 2 s and consists of three p orbitals of equal energy .

The long axis of each dumbbell-shaped p orbitals is perpendicular to the other two. It is convenient to label the axes 2 p x , 2 p y , and 2 p z . The third principal energy level ( n =3) has three sublevels, called 3 s , 3 p , and 3 d . The 3 d sublevel consists of five d orbitals of equal energy. Thus the third principal energy level has nine orbitals (one 3 s , three 3 p , and five 3 d orbitals). The fourth principal energy level ( n =4) has four sublevels, called 4 s , 4 p , 4 d , and 4 f . The 4 f sublevels consist of seven f orbitals of equal energy. The fourth principal energy level, then, has 16 orbitals (one 4 s , three 4 p , five 4 d , and seven 4 f orbitals).

Electron Configuration In most general phenomena, change proceeds towards the lowest possible energy. High-energy systems are unstable. Unstable systems lose energy to become more stable. In the atom, electrons and the nucleus interact to make the most stable arrangement possible. The ways in which electrons are arranged around the nuclei of the atoms are called electron configurations. Three rules - the aufbau principle, the Pauli exclusion principle, and Hund’s rule - tell you how to find the electron configurations of atoms.

1. Aufbau principle: Electrons enter orbitals of lowest energy first. The various orbitals within a sublevel of a principal energy level are always of equal energy . Further, within a principal energy level the s sublevel is always the lowest-energy sublevels . Yet the range of energy levels within a principal energy level can overlap the energy levels of adjacent principal level . Electrons enter the orbitals of lowest energy first. Note that the filling of atomic orbitals does not follow a simple pattern beyond the second energy level. For example, the 4 s orbital is lower in energy than a 3 d orbital.

Is a 4 f orbital higher or lower in energy than a 5 d orbital? This is shown on the aufbau diagram of Figure 13.6 on the previous page. Each box represents an atomic orbital.

2. Pauli exclusion principle: An atomic orbital may describe at most two electrons. For example, either one or two electrons can occupy an s orbital or a p orbital. To occupy the same orbital, two electrons must have opposite spins; that is the electron spins must be paired. Spin is a quantum property of electrons and may be clockwise or counterclockwise. A vertical arrow indicates an electron and its direction of spin ( or ). An orbital containing paired electrons is written as .

3. Hund’s rule: When electrons occupy orbitals of equal energy, one electron enters each orbital until all the orbitals contain one electron with parallel spins. Second electrons then add to each orbital so their spins are paired with the first electrons. Thus each orbital can eventually have two electrons with paired spins. For example, three electrons would occupy three orbitals of equal energy as follows : .

Physics and the Quantum Mechanical Model The previous sections in this chapter introduced you to some ideas about atomic structure. You also learned how to write electron configurations for atoms. In the remainder of the chapter, you will backtrack a bit to delve further into the work that led to the development of Schrödinger’s equation and the quantum mechanical model of the atom. Rather curiously, this model grew out of the study of light.

Isaac Newton (1642-1727) thought of light as consisting of particles. By the year of 1900, however, most scientists accepted the idea that light was a wave phenomenon . According to the wave model, light consists of electromagnetic waves. Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, x-rays, and gamma rays. Figure 13.8 shows a typical wave. All electromagnetic waves travel in a vacuum at the speed of 3.0 x 10 10 cm/s (3.0 x 10 8 m/s) Each complex wave cycle begins at the origin, then returns to the origin.

The amplitude of a wave is the wave’s height from the origin to the crest. The wavelength (λ, the Greek letter lambda) is the distance between the crests. Frequency ( v , the Greek letter nu) is the number of wave cycles to pass a given point per unit of time. The frequency and the wavelength of all waves, including light, are inversely related. As the wavelength of light increases, for example, the frequency decreases. The product of frequency and wavelength always equals a constant (c), the speed of light; that is, c= λ ν

The units of frequency are usually cycles per second. The SI unit of cycles per second is called a hertz (Hz). Sunlight consists of light with a continuous range of wavelengths and frequency. The wavelength and frequency of each color of light are characteristic of that color. When sunlight passes through a prism, the different wavelengths separate into a spectrum of colors. A rainbow is an example of this phenomenon. Each color blends into the next in the order red, orange, yellow, green, blue, indigo, and violet. In the visible spectrum, as shown in figure 13.10, red light has the longest wavelength and the lowest frequency .

Every element emits light when it is excited by the passage of an electric discharge through its gas or vapor. The atoms first absorb energy, then lose the energy as they emit light. Passing the light emitted by an element through a prism gives the atomic emission spectrum of the element. The emission spectra of elements are quite different from the spectrum of white light. Each line in an emission spectrum corresponds to one exact frequency of light emitted by the atom. Therefore each line corresponds to a specific amount of energy being emitted.

The emission spectrum of each element is unique to that element. This makes such a spectra extremely useful for the identification of unknown or inaccessible substances.

The Quantum concept and the Photoelectric Effect The seeds of an idea that explained atomic spectra came in 1900 from the German physicist Max Planck (1858-1947). Planck was trying to describe quantitatively why a body such as a chunk of iron appears to change in color as it is heated. First it is appears black, then red, yellow, white, and blue as its temperature increases, as shown in Figure 13.14.

Planck found he could explain the color changes if he assumed that the energy of a body changes only in small discrete units. You can think of these discrete units as bricks used to build a wall- a brick wall can only increase or decrease in size in increments of one or more bricks. Planck showed mathematically that the amount of radiant energy ( E ) absorbed or emitted by a body is proportional to the frequency of the radiation ( v ). E = h x v The constant ( h ) in the above equation is called Planck’s constant, which has a value of 6.6262 x 10 -34 J • s (J is the joule, the SI unit of energy.) The energy of a quantum equals h x v .

Any attempt to increase or decrease the energy of a system by a fraction of h x v must fail. A small energy change involves the emission or absorption of low-frequency radiation. A large energy change involves the emission or absorption of high-frequency radiation. Planck’s proposal that quanta of energy are absorbed or emitted was revolutionary. Everyday experiences had led people to believe that there was no limitation to the smallness of permissible energy changes in a system. It appears, for example, that thermal energy may be continuously supplied to heat liquid water to any temperature between 0° C and 100º C.

Actually, the water temperature increases by infinitesimally small steps, which occurs as individual molecules absorb quanta of energy. An ordinary thermometer is unable, however, to detect such small changes in temperature. Thus your everyday experiences gives you no clue to the fact that energy is quantized. In 1905 Albert Einstein, then a patent examiner in Zurich, Switzerland, returned to Newton’s idea of particles of light. Einstein proposed that light could be described as quanta of energy that behave as if they were particles. Light quanta are called photons.

The energy of photons is quantized according to the equation E= h x v .

An Explanation of Atomic Spectra Consider the lone electron of a hydrogen atom in its lowest energy level, or ground state . In the ground state, the quantum number ( n ) is 1. Excitation of the electron raises it to an excited state so that n = 2, 3, 4, and so on. If the energy levels are quantized, it takes a quantum of energy ( h x v ) to raise the electron from the ground state to an excited state. The same amount of energy is emitted as a photon when the electron drops from the excited state to the ground state.

Only electrons in transition from higher to lower energy levels lose energy and emit light.

Models

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