Atomic Radius

Last Updated : 25 Feb, 2024

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

Atomic Radius Definition

Atomic radius of an atom is defined as the total distance from nucleus of atom to the outermost orbit in which electron is revolving.

Atomic Radius Example

For Example, the atomic radius of Hydrogen is 53 pm it means, the distance between the center of the hydrogen atom and its outermost orbit is 53 pm.

Atomic Radius Meaning

Atomic Radius is the distance between the center of the atom to the outermost shell of the atom. Atoms are made up of three subatomic particles namely – electron, proton, and neutron. Protons and Neutrons are present in the center of the atom inside the nucleus. Nucleus is present in the center of the atom. Proton tightly bounded together. Electrons revolve around the nucleus in a defined circular path known as orbit. The overall structure of an atom is assumed to be in circular shape. Atomic radius is generally measured in Picometer. Atomic Radius gives the idea about the atomic size. Atomic Radius is measured in the power of 10^-9 to 10^-12. The plural form of Atomic Radius is Atomic Radii.

Atomic-Radius

How to get Atomic Radius?

The radius of atom can be measured by the finding distance between the nuclei of two touching atoms then dividing it by 2. Atomic radius is also measured by calculating the distance between the center of the nucleus of an atom and its outermost shell. Atomic radius is measured in order of 10^-12to 10^-15 meter. Since, as per quantum mechanical model the electron around atom is in the form of cloud, hence its doesn’t have defined boundary. In such case, the atomic radius is calculated by dividing the distance between two successive nucleus by 2.

The calculation of atomic radius is a complicated process because electron form cloud shell outside nucleus and does not have any fixed shape. The electron in an atom experiences repulsive and attractive force which make it more difficult to precisely calculate the atomic radius and thus atomic size of an atom. However, Bohr attempted and gave formula for single electron system of atom to precisely calculate its radius. This formula can be used to get an idea of radius in multi electron atom. Let’s learn the atomic radius formula

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.

F_c = 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 × n²where n is nth number of orbit

So, Radius = 0.529 Å × n²

Note: Above Bohr’s Formula is valid for only hydrogen like-atom.

Types of Atomic Radius

There are different types of Atomic radii based on type of atom and type of bonding present in them. Some types of atomic radii is defined below:

Metallic Radius

Metallic radius is defined as half the distance between nuclei of two atom in a metallic crystal structure. Simply, Metallic radius is present in metals. for example metallic radii is defined in metals such as sodium, potassium, calcium etc. Francium is the metal present in periodic table which has largest metallic radius among all the elements.

Metallic radius = 1/2(internuclear distance between two atom in a metallic crystal structure)

Covalent Radius

Covalent radius is defined as the half the distance between the nuclei of two covalently bonded atoms of the same element in a molecule. It is half of distance between two nucleus of atom which are covalently bonded in a molecule. Generally covalent radius is formed in non-metals.

Covalent radius = 1/2(internuclear distance between two covalently bonded atom)

Van der Waals Radius

Van der Waals radius is defined as half of distance present between the nuclei of two non bonded adjacent atoms in a molecule. Van der Waals radius is mainly present in gaseous state because their atom moves freely without bonding. Van der Waals radius can never be measured in solid and liquid state because their atom are bonded tightly with one another.

Ionic Radius

Ionic radius is defined as the distance distance between the nucleus of an ion up to which it has an influence on its electron cloud. Ionic radius is similar to atomic radius. The difference is that Ionic radius is the radius of an electrically charged atom, whereas atomic radius is the radius of a neutral atom.

Atomic Radius of Some Common Elements

Atomic radius of elements is usually measured in picometer. Atomic radius of some commonly elements are listed below:

Atomic Radius of Hydrogen(H)

Atomic radius of hydrogen atom is 53 pm. It’s atomic number is 1. Hydrogen is first element of periodic table.

Atomic Radius of Sodium(Na)

Atomic radius of sodium is 0.190 nm (190 pm). Sodium is metal with Atomic Number 11. Sodium is an Alkali Metal that lies in Group 1 and period 3 in the periodic table.

Atomic Radius of Potassium(K)

Atomic radius of potassium is 0.235 nm (253 pm) and the ionic radius is 0.133 nm. Atomic number of potassium is 19 and its atomic symbol is K.

Atomic Radius of Argon(Ar)

Atomic radius of Argon is 0.098 nm. Argon is noble gas whose atomic number is 18, a stable electronic configuration.

Atomic Radius of Copper(Cu)

Atomic radius of copper is 128 pm. Copper is represented by atomic symbol Cu(Atomic number 29). Copper is a metal from group 11.

Atomic Radius of Oxygen(O)

Atomic Radius of Oxygen is 0.073 nm (73 nm). Oxygen has the Atomic Number 8 and its mass number is 16. Oxygen lies in the 16th group of the Periodic Table

Atomic Radius of Carbon(C)

Atomic Radius of Carbon is 0.0914 nm (91.4 pm). Carbon is the most versatile element. The atomic number of Carbon is 6 and its mass number is 12.

Largest Atomic Radius

Francium (Atomic number 87) has largest radius in periodic table. The atomic radius of francium is 348 pm.

Atomic Radius Chart

Below is the chart where atomic radii of some metals, non-metals and metalloid are given below:

Elements	Atomic Radius
Argon	0.098 nm
Potassium	0.235 nm
Calcium	0.197 nm
Sodium	0.190 nm
Copper	128 pm
Hydrogen	53 pm
Helium	0.208 nm
Francium	348 pm
Silicon	0.132 nm
Carbon	0.0914 nm

Atomic Radius Trend

Atomic Radius of Element in periodic table vary in a systematic manner across the groups and periods. Let’s learn the Priodic variation of Atomic Radius in detail.

Atomic Radius Across Group

Atomic radius increases as we move from top to bottom in a group because number of shells increases due to increase in number of electrons. As the number of shells increases the size of atom also increases.

Atomic Radius Across Period

Atomic radius decreases as we move from left to right in a period due to increase in effective nuclear charge (The nuclear charge is the total charge in the nucleus of all the protons). As the number of protons increases, nuclear charge increases which shrink the size of atom.

Atomic Radius vs Ionic Radius

Atomic Radius and Ionic Radius are two most common terms used for determining the atomic size. The term atomic radius signifies the size of an atom in its ground state while the term ionic radius signifies the size of an atom after it has lost or gained electron i.e. in its ionic state. The basic difference between Atomic and Ironic Radius is tabulated below:

Atomic Radius	Ionic Radius
The radius of a neutral atom is called the atomic radius.	The radius of an atom’s ion is known as the ionic radius.
Atomic radius can be estimated as the distance between the nucleus of atom and outermost electron boundary.	The atomic radius of cations is less than that of anions.
Atomic radius is determined only for neutral gaseous atom.	Ionic radius is determined considering cations and anions in ionic bond

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Atomic Radius – FAQs

1. What is the Atomic Radius of an Atom?

The atomic radius of an atom is the distance from the center of the nucleus to the outermost shell of the atom

2. Which has Largest Atomic Radius?

Francium(Atomic number: 87) has largest radius in periodic table. The atomic radius of francium is 348 pm.

3. Which Element has the Smallest Atomic Radius?

Helium(Atomic number: 2) has smallest atomic radius. The atomic radius of a helium atom is 31 pm.

4. Which among them is largest Radius: Metallic Radius, Covalent Radius or Van der Waals radius?

Van der Waal radius is largest among all of them because van der Waals radius is defined between two adjacent non bonded atoms in a molecule.

5. What is definition of Atomic Radius?