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How to Calculate Particle Shapes

The shape of an atom is defined by the shape of its atomic orbitals. An orbital is a region around the nucleus of an atom where its electrons are most likely to be found. The electron configuration of an atom is a series of letters and numbers that show the electrons in each orbital. The letters are the names of the energy shells, which are regions containing the orbitals. The numbers in front of the letters denote the orbital within a given energy shell, while the superscripted numbers behind those letters are the number of electrons in that orbital.

Instructions

    • 1

      Draw a circle on paper. This circle is orbital 1s, which is the first orbital in the s-shell. An electron configuration whose first term is 1s2 has two atoms in this orbital.

    • 2

      Draw the p-orbitals, each of which has the form of two teardrop-shapes whose points meet at the nucleus. Draw a 3-dimensional set of axes, labeled X, Y, and Z, to show how each orbital is arranged. The p-x orbital is situation horizontally along the x-axis; the p-y orbital is perpendicular to the p-x orbital and lies horizontally along the y-axis; the p-z orbital is perpendicular to the x and y axes and is vertical.

    • 3

      Draw the first d-orbital, which is shaped like the p-orbitals but has an elliptical disc-shaped region in between the two teardrop-shape regions. This orbital lies along the z-axis, and the disc-shaped region in the center is intersected laterally -- “cut in half,” so-to-speak -- by the plane formed by the x and y axes. This is the most complicated of the d-orbitals.

    • 4

      Draw the d-xy, d-yz, and d-xz orbitals, which look somewhat like the p-orbitals but which are made up of four teardrop-shaped regions rather than two, which are arranged in a manner suggestive of a clover leaf; these four regions do not meet at the nucleus, but are spaced away from it. The d-xy orbital has two regions lying along the y-axis in a similar manner to the p-orbitals, with its other two regions lying along a line that bisects the angle between the y and x axes; one of these regions points slightly upward along the z-axis, while the other points slightly downward. This configuration repeats in analogous fashion for the d-yz and d-xz regions.

    • 5

      Draw the d(x^2)-(y^2) orbital. The x^2 and y^2 notation should be taken merely as superscripted numbers, not exponents as in algebra. It is shaped similarly to the other d-orbitals, with two of its regions lying along the x-axis. It has two other regions lying along the y-axis, rather than the line between the x and y axes; one of these regions points slightly down, the other up.

    • 6

      Fill out each shell by labeling each orbital with the number electrons given in the atom's electron configuration. Not all of the orbitals will always be filled, so erase any orbital with no electrons. Pay special attention to the outermost shell, as this is the shell containing the so-called “valence” electrons, which determine the reactivity of a given atom.

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