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The Bohr radius is consequently known as the "atomic unit of length". It is often denoted by a 0 and is approximately 53 pm. Hence, the values of atomic radii given here in picometers can be converted to atomic units by dividing by 53, to the level of accuracy of the data given in this table.
In quantum mechanics, an atomic orbital (/ ˈ ɔːr b ɪ t ə l / ⓘ) is a function describing the location and wave-like behavior of an electron in an atom. [1] This function describes an electron's charge distribution around the atom's nucleus, and can be used to calculate the probability of finding an electron in a specific region around ...
The Bohr radius is defined as [3] = =, where . is the permittivity of free space,; is the reduced Planck constant,; is the mass of an electron,; is the elementary charge,; is the speed of light in vacuum, and
The atomic radius of each element generally decreases across each period due to an increasing number of protons, since an increase in the number of protons increases the attractive force acting on the atom's electrons. The greater attraction draws the electrons closer to the protons, decreasing the size of the atom.
Later studies found an empirical relation between the charge radius and the mass number, A, for heavier nuclei (A > 20): R ≈ r 0 A 1/3. where the empirical constant r 0 of 1.2–1.5 fm can be interpreted as the Compton wavelength of the proton. This gives a charge radius for the gold nucleus (A = 197) of about 7.69 fm. [8]
Charge number (denoted z) is a quantized and dimensionless quantity derived from electric charge, with the quantum of electric charge being the elementary charge (e, constant). The charge number equals the electric charge ( q , in coulombs ) divided by the elementary charge: z = q / e .
The charge is now interpreted as the electron charge, , and the energy is set equal to the relativistic mass–energy of the electron, , and the numerical factor 3/5 is ignored as being specific to the special case of a uniform charge density. The radius is then defined to be the classical electron radius, , and one arrives at the expression ...
It is now apparent why Rydberg atoms have such peculiar properties: the radius of the orbit scales as n 2 (the n = 137 state of hydrogen has an atomic radius ~1 μm) and the geometric cross-section as n 4. Thus, Rydberg atoms are extremely large, with loosely bound valence electrons, easily perturbed or ionized by collisions or external fields.