Probability cloud

Figure 2.15 shows the corresponding probability clouds )I2 that... 

PROBABILITY CLOUDS AND ATOMIC ORBITALS HELP US VISUALIZE ELECTRON WAVES... 

Electron waves are three-dimensional, which makes them difficult to visualize, but scientists have come up with two ways of visualizing them as probability clouds and as atomic orbitals. 

A probability cloud is therefore a close approximation of the actual shape of an electrons three-dimensional wave. 

An atomic orbital, like a probability cloud, specifies a volume of space where the electron is most likely to be found. By convention, atomic orbitals are drawn to delineate the volume inside which the electron is located 90 percent of the time. This gives the atomic orbital an apparent border, as shown in Figure 5.17b. This border is arbitrary, however, because the electron may exist on either side of it. Most of the time, though, the electron remains within the border. 

Probability clouds and atomic orbitals are essentially the same thing. They differ only in that atomic orbitals specify an outer limit, which makes them easier to depict graphically. 

Probability cloud The pattern of electron positions plotted over time to show the likelihood of an electrons being at a given position at a given time. 

What do probability clouds and atomic orbitals help us visualize ... 

If the two atoms in a covalent bond are identical, their nuclei have the same positive charge, and therefore the electrons are shared evenly. We can represent these electrons as being centrally located by using an electron-dot structure in which the electrons are situated exactly halfway between the two atomic symbols. Alternatively, we can draw a probability cloud (see Section 5-5) in which the positions of the two bonding electrons over time are shown as a series of dots. Where the dots are most concentrated is where the electrons have the greatest probability of being located ... 

Atomic orbitals represent the electron probability clouds of an atom s electrons. Q The spherical 1s and 2s orbitals are shown here. All s orbitals are spherical in shape and increase in size with increasing principal quantum number. The three dumbbell-shaped p orbitals are oriented along the three perpendicular X, y, and z axes. Each of the p orbitals related to an energy sublevel has equal energy. 

The atomic number determines the identity of an element because the chemical properties of an element are almost exclusively due to its electrons. The quantum mechanical model, which was first proposed in the 1920s, treats matter as if it had wavelike characteristics. Solution of the Schrodinger wave equation for an atom yields a set of mathematical wave functions that can be related to the probabilities of locating the electrons both spatially and energetically. This function, when plotted in three-dimensional space, generates a probability cloud. We cannot be absolutely certain where the electron will be at any instant, but we do know the region of space that is most probably occupied over time. 

The parameter is obtained in two steps— the first is averaging all possible positions in the particle from which a vector r can start and be within the particle, and the second step is determining the probability that a randomly directed vector r from an arbitrary starting point in the particle will fall in the particle (Clatter and Kratky 1982). The probability p(r) in the vicinity of r (the particle size) can be graphically represented by a Caussian probability cloud created by the summation of all possible positions of the particle where the center of the probability cloud is in the particle phase. 

The d orbitals are more complex in shape and arrangement in space. In 1925 Touis de Broglie suggested that electrons behaved like waves. This led to the idea of electron probability clouds. The electron probability cloud for one type of d orbital is very strange -it is like a modified p orbital with a ring around the middle (Figure 3.8). You will not need to know the d-orbital shapes at AS level, but you will for A level when studying the transition elements (see Chapter 24). 

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