D4.2 Periodic Variation in Atomic Radius
Given that electron density is distributed throughout space but concentrated near the nucleus, it is hard to define the size of an atom. Typically, chemists think of atoms as spheres with radii on the order of tens to hundreds of picometers. One way to determine atomic radii is to measure the distance between atomic nuclei in homonuclear diatomic molecules. (Homonuclear means two atoms of the same element bonded to each other.) The radius of one atom is half the internuclear distance. A second way is to measure the distance between the nuclei of two atoms in a solid metal, where each atom touches several nearest neighbors. Once a set of atomic radii has been determined, these values can be used to estimate the lengths of bonds that have not yet been measured.
Here are three correct statements about the atomic radii plotted against atomic number in the Figure above. In your notebook write a clear, concise explanation for why each statement is true.
- There is a large increase in atomic radius going from a noble-gas element to the following group 1 (IA) element.
- Within each period, such as the elements from Na to Ar, atomic radius decreases as atomic number increases.
- Within a periodic group, such as group 1 (IA), atomic radius increases going down the periodic table.
Write in your notebook, then left-click here for an explanation.
Statement 1: Each noble gas has an electron configuration with a complete octet in its outermost shell. Each group 1 (IA) element has one more electron than the noble gas and the electron is in an s orbital with n value one more than the noble gas The last electron added to build up a group 1A atom’s electron configuration is in a larger shell and, on average, farther from the nucleus. Thus, the group 1 (IA) atom is a larger sphere with a larger radius than the noble gas.
For example, compare the noble gas neon, Ne (1s22s22p6), with the next element sodium, Na (1s22s22p63s1). In sodium there is an electron in the 3s orbital, which is much larger than the n = 2 orbitals (the largest orbitals in neon). Radii are Ne = 68 pm, Na = 191 pm.
Statement 2: Within a period, going from left to right across the periodic table from one element to the next, an electron is added to the same shell and the nuclear charge increases by one. Electrons in the same shell are about the same distance from the nucleus so the probability that an electron in the same shell is between the nucleus and another electron in the shell is small. Because electrons in the same shell screen each other incompletely, the effective nuclear charge increases. The larger effective nuclear charge attracts electron density closer to the nucleus, so the atomic radius decreases.
Statement 3: From one element to the next going down any group in the periodic table the principal quantum number, n, increases. This results in larger and larger electron-density distributions, so the size of the atom increases. For group 1 (IA), the radii are H = 37 pm, Li = 157 pm, Na = 191 pm, K = 235 pm, Rb = 250 pm, and Cs = 272 pm.
Exercise: Predicting Atomic Radii
Exercise: Atomic Radii and Periodic Table
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