Van der Waals radius

The van der Waals radius is the distance, where the attractive and repulsive forces between the two nonbonded atoms are equal.

The Van der Waals radius is equal to one half the distance between two unbonded atoms when the electrostatic forces between them are balanced. In other words, it is half of the closest distance between two atoms that aren't bonded or within the same molecule. Picometers (pm) are typically the unit used to report the value.

The distance reflects the action of intermolecular forces (e.g., dipole-dipole and dispersion forces) and is related to van der Waals interactions. Knowing the van der Waals radius is helpful when predicting how closely atoms will pack to form a solid.

Van der Waals radius is measured in the nonbonding state. It can't be measured in the liquid and solid-state as the atoms are bonded to each other in such state.

Therefore Van der Waals radius is measured only in the gaseous state.

Definition 2

What is Van Der Waals Radius 

The Van der Waals radius is a measure of the effective size of an atom or molecule. It is defined as half the distance between the nuclei of two adjacent, non-bonded atoms of the same element in a solid or molecular crystal when they are at their closest approach without any significant repulsive forces between them. In simpler terms, it represents the distance at which two atoms, if they were not bonded, would come closest to each other due to the attractive and repulsive forces between their electron clouds.

For example, imagine two helium (He) atoms that are not chemically bonded but are brought close together in a solid. At a certain distance, the attractive forces between their electron clouds dominate, causing them to approach each other. However, if they get too close, the repulsive forces between the electron clouds and the positively charged nuclei start to push them apart. The Van der Waals radius for helium represents the equilibrium distance at which these attractive and repulsive forces are balanced.

Role of Van Der Waals Radius 

The Van der Waals radius holds significant importance in the realms of chemistry and physics, playing a pivotal role in various key areas. Firstly, it is central to understanding intermolecular forces, where the balance between attractive London dispersion forces and repulsive forces, regulated by the Van der Waals radius, dictates whether atoms or molecules form bonds or engage in weak interactions. In the solid state, the Van der Waals radius becomes crucial for molecular packing in a crystal lattice, determining packing efficiency and crystal structure across various materials. Additionally, the Van der Waals equation of state, incorporating the Van der Waals radius, is instrumental in analyzing the behavior of real gases. This equation provides corrections for the finite size of gas molecules, particularly at high pressures and low temperatures, explaining deviations from ideal gas behavior.

Covalent radius Vs Van der Waals radius

Covalent radius is half of the internuclear separation between the nuclei of two single-bonded atoms of the same species (homonuclear). 

While van der Waals radius is used to define half of the distance between the closest approach of two non-bonded atoms of a given element.

Van der Waals radii can be used to study nonbonded (especially intermolecular) interactions.

https://pediaa.com/what-is-the-difference-between-van-der-waals-radius-and-covalent-radius/#Van%20Der%20Waals%20Radius

Here’s a list of the van der Waals radii of the periodic table elements by atomic number: Atomic Number Element Van der Waals Radius (pm) 1 Hydrogen 120 2 Helium 140 3 Lithium 182 4 Beryllium 153 5 Boron 192 6 Carbon 170 7 Nitrogen 155 8 Oxygen 152 9 Fluorine 147 10 Neon 154 11 Sodium 227 12 Magnesium 173 13 Aluminum 184 14 Silicon 210 15 Phosphorus 180 16 Sulfur 180 17 Chlorine 175 18 Argon 188 19 Potassium 275 20 Calcium 231 21 Scandium 212 22 Titanium 206 23 Vanadium 200 24 Chromium 192 25 Manganese 192 26 Iron 190 27 Cobalt 188 28 Nickel 169 29 Copper 140 30 Zinc 139 31 Gallium 185 32 Germanium 210 33 Arsenic 185 34 Selenium 185 35 Bromine 188 36 Krypton 202 37 Rubidium 303 38 Strontium 262 39 Yttrium 248 40 Zirconium 206 41 Niobium 198 42 Molybdenum 193 43 Technetium 188 44 Ruthenium 187 45 Rhodium 185 46 Palladium 180 47 Silver 160 48 Cadmium 158 49 Indium 193 50 Tin 217 51 Antimony 207 52 Tellurium 207 53 Iodine 198 54 Xenon 216 55 Cesium 303 56 Barium 266 57 Lanthanum 271 58 Cerium 251 59 Praseodymium 249 60 Neodymium 244 61 Promethium 245 62 Samarium 244 63 Europium 245 64 Gadolinium 244 65 Terbium 243 66 Dysprosium 240 67 Holmium 240 68 Erbium 239 69 Thulium 238 70 Ytterbium 237 71 Lutetium 263 72 Hafnium 207 73 Tantalum 204 74 Tungsten 198 75 Rhenium 193 76 Osmium 190 77 Iridium 189 78 Platinum 175 79 Gold 166 80 Mercury 202 81 Thallium 207 82 Lead 202 83 Bismuth 207 84 Polonium 202 85 Astatine 202 86 Radon 220 87 Francium 270 88 Radium 215 89 Actinium 200 90 Thorium 175 91 Protactinium 175 92 Uranium 186 93 Neptunium 186 94 Plutonium 187 95 Americium 188 96 Curium 189 97 Berkelium 190 98 Californium 191 99 Einsteinium 192 100 Fermium 193 101 Mendelevium 194 102 Nobelium 195 103 Lawrencium 196 104 Rutherfordium 197 105 Dubnium 198 106 Seaborgium 199 107 Bohrium 200 108 Hassium 201 109 Meitnerium 202 110 Darmstadtium 203 111 Roentgenium 204 112 Copernicium 205 113 Nihonium 206 114 Flerovium 207 115 Moscovium 208 116 Livermorium 209 117 Tennessine 210 118 Oganesson 211 Note: The values are approximate and can vary based on different sources. Some noble gases do not have defined van der Waals radii as they do not typically form van der Waals interactions.