Atomic Radius Formula
Atomic radius of any element is inversely proportional to its Atomic Number. Because , as atomic number increases effective nuclear charge increases which reduces the size of atom. The formula for Atomic radius of any element is given by :
Atomic Radius = 0.529Å × n2/z
where, Z is Atomic Number
Formula for Atomic Radius of Hydrogen by Bohr’s Formula
Atomic radius of every element can be calculated by using bohr’s formula which is derived below:
The angular momentum given by bohr’s formula is
mvr = nh/2π
where,
- n is he Number of orbit in which electron is moving
- h is the Plank’s Constant
- m is the Mass of Electron
- v is the Velocity of Electron
- r is the Radius of Outermost Electron
when an electron is moving in a circular orbit, it moves because it possesses centripetal force. Centripetal force is defined as: The force which allows an object or an electron to move in a circular orbit is called centripetal force.
Fc = mv2/r ……(1)
So, electrostatic force of attraction is given by
Electrostatic force = Ze2/4π∈or2 ……..(2)
Where ∈o is the relative permittivity and its value is 8.84 × 10-12 C2J-1m-1.
Equating the above two equation (1) and (2) we get,
mv2/r = Ze2/4π∈or2
mv2 = Ze2r/4π∈0r2
mv2 = Ze2/4π∈0r
r = Ze2/4π∈0mv2……(3)
Now from equation mvr = nh/2π
v = nh / 2πmr
By taking square on both sides
v2 = n2h2 / 4π2m2r2
putting the value of r from eqn. (3)
r = Ze2/4π∈0m (n2h2 / 4π2m2r2)
r = Ze24π2m2r2/4π∈0mn2h2
= Ze2πmr/∈o n2h2
r = ∈0n2h2/Ze2πm
r = (∈0h2/Ze2πm)n2 putting the value of constant (∈0h2/Ze2πm) = 0.529 × 10-10 m
Putting the value of constant: r = 0.529Å × n2 where n is nth number of orbit
So, Radius = 0.529 Å × n2
Note: Above Bohr’s Formula is valid for only hydrogen like-atom.
Atomic Radius
Atomic Radius is defined as the total distance between the center of the atom to the outermost orbit in which the electron is revolving. Atomic Radius tells about the atomic size. Since Atoms are considered to be spherical, the size of an atom can be calculated by measuring its radius. Atomic radius is necessary to understand the behavior and properties shown by atoms. Some of the properties of an atom are affected by atomic radius.
In this article, we are going to learn about atomic radius, types of atomic radius, the atomic radius chart of some common elements, trend of atomic radius in the periodic table in detail.
Table of Content
- Atomic Radius Definition
- Atomic Radius Formula
- Types of Atomic Radius
- Atomic Radius of Some Common Elements
- Atomic Radius Chart