How does atomic radius vary down group 2?

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Learning outcomes
Atomic radius
Description of trend
Explanation of this trend
While going along the period the number of electrons increases for the same number of shells so the effective nuclear charge increases in the elements and as a result the outermost electron will be more strongly attached to the central nucleus. This decreases the radius of the elements that go from left to right.On the other hand, the atomic radius generally increases down a group. This is because, down a group, the principal quantum number (n) increases which results in an increase in the distance between the nucleus and valence electrons.
How can all of these people fit in such a small space?
Atomic Radius
Periodic Trend
Group Trend
Why does atomic radius increase down group 2?
How does atomic radius vary across period 2?
How does atomic radius vary down the group 1 and group 2?
Why does atomic radius decrease across a period 2?

Learning outcomes

After studying this page, you should be able to:

describe and explain the trend in atomic radius down group 2

Atomic radius

The table shows atomic radius values for the common elements in group 2 (the alkaline earth metals).

Element	Symbol	Atomic number	Atomic radius /nm
beryllium	Be	4	0.125
magnesium	Mg	12	0.160
calcium	Ca	20	0.174
strontium	Sr	38	0.191
barium	Ba	56	0.198

Atomic radius is the distance from the centre of the nucleus to the edge of the surrounding electron cloud. It is measured or calculated in different ways, so values vary from source to source.

Description of trend

The graph shows how atomic radius varies down group 2:

as the atomic number increases, the atomic radius increases.

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Explanation of this trend

Going down group 2:

there are more filled shells between the nucleus and the outer electrons …
the outer electrons are more shielded from the attraction of the nucleus …
so the electrons in the higher energy levels are further from the nucleus …
the atomic radius increases.

You might expect the atomic radius to decrease because the nuclear charge increases going down the group. However, this does not happen: although the electrons in the inner shells become closer to the nucleus, the factors described in the Explanation have a greater influence overall.

While going along the period the number of electrons increases for the same number of shells so the effective nuclear charge increases in the elements and as a result the outermost electron will be more strongly attached to the central nucleus. This decreases the radius of the elements that go from left to right.On the other hand, the atomic radius generally increases down a group. This is because, down a group, the principal quantum number (n) increases which results in an increase in the distance between the nucleus and valence electrons.

How does atomic radius vary in a period and in a group? How do you explain the variation?

Atomic radius generally decreases from left to right across a period. This is because within a period, the outer electrons are present in the same valence shell and the atomic number increases from left to right across a period, resulting in an increased effective nuclear charge. As a result, the attraction of electrons to the nucleus increases.

On the other hand, the atomic radius generally increases down a group. This is because down a group, the principal quantum number (n) increases which results in an increase of the distance between the nucleus and valence electrons.

Within a group Atomic radius increases down the group.

Reason. This is due to continuous increases in the number of electronic shells or orbit numbers in the structure of atoms of the elements down a group.

Variation across period.

Atomic Radii. From left to right across a period atomic radii generally decreases due
to increase in effective nuclear charge from left to right across a period.

Concept: Physical Properties - Atomic Radius

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Figure \(\PageIndex{1}\) (Credit: James Cridland; Source: http://www.flickr.com/photos/jamescridland/613445810/(opens in new window); License: CC by 2.0(opens in new window))

How can all of these people fit in such a small space?

Events draw large numbers of people to them. Even an outdoor event can fill up so that there is no room for more people. The crowd capacity depends on the amount of space in the venue, and the amount of space depends on the size of the objects filling it. We can get more people into a given space than can elephants, because elephants are larger than people. We can get more squirrels into that same space than we can people for the same reason. Knowing the sizes of objects to be dealt with can be important in deciding how much space is needed.

Atomic Radius

The size of atoms is important to explanations of the behavior of atoms or compounds. One way to express the size of atoms is by use of atomic radius. This data helps us understand why some molecules fit together and why other molecules have parts that get too crowded under certain conditions.

The size of an atom is defined by the edge of its orbital. However, orbital boundaries are fuzzy, and variable under different conditions. In order to standardize the measurement of atomic radii, the distance between the nuclei of two identical atoms bonded together is measured. The atomic radius is defined as one-half the distance between the nuclei of identical atoms that are bonded together.

Figure \(\PageIndex{2}\): The atomic radius \(\left( r \right)\) of an atom can be defined as one half the distance \(\left( d \right)\) between two nuclei in a diatomic molecule. (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC BY-NC 3.0(opens in new window))

Atomic radii have been measured for elements. The units for atomic radii are picometers, equal to \(10^{-12}\) meters. As an example, the internuclear distance between the two hydrogen atoms in an \(\ce{H_2}\) molecule is measured to be \(74 \: \text{pm}\). Therefore, the atomic radius of a hydrogen atom is \(\frac{74}{2} = 37 \: \text{pm}\).

Figure \(\PageIndex{3}\): Atomic radii of the representative elements measured in picometers. (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC BY-NC 3.0(opens in new window))

Periodic Trend

The atomic radius of atoms generally decreases from left to right across a period. There are some small exceptions, such as the oxygen radius being slightly greater than the nitrogen radius. Within a period, protons are added to the nucleus as electrons are being added to the same principal energy level. These electrons are gradually pulled closer to the nucleus because of its increased positive charge. Since the force of attraction between nuclei and electrons increases, the size of the atoms decreases. The effect lessens as one moves further to the right in a period, because of electron-electron repulsions that would otherwise cause the atom's size to increase.

Group Trend

The atomic radius of atoms generally increases from top to bottom within a group. As the atomic number increases down a group, there is again an increase in the positive nuclear charge. However, there is also an increase in the number of occupied principal energy levels. Higher principal energy levels consist of orbitals which are larger in size than the orbitals from lower energy levels. The effect of the greater number of principal energy levels outweighs the increase in nuclear charge, and so atomic radius increases down a group.

Figure \(\PageIndex{4}\): A graph of atomic radius plotted versus atomic number. Each successive period is shown in a different color. As the atomic number increases within a period, the atomic radius decreases. (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC BY-NC 3.0(opens in new window))

Summary

Atomic radius is determined as half the distance between the nuclei of two identical atoms bonded together.
The atomic radius of atoms generally decreases from left to right across a period.
The atomic radius of atoms generally increases from top to bottom within a group.

Review

Define “atomic radius.”
What are the units of measurement for atomic radius?
How does the atomic radius of different elements change across a period?
How does atomic radius change from top to bottom within a group?
Explain why the atomic radius of hydrogen is so much smaller than the atomic radius of potassium.

Why does atomic radius increase down group 2?

Atomic radius increases down Group 2. As one goes down the group, the atoms have more shells of electrons making the atom bigger and there is a decrease in effective nuclear charge with successive elements because of increased screening, and so the electrons are less firmly held to the nucleus.

How does atomic radius vary across period 2?

The atomic radius of atoms generally decreases from left to right across a period. The atomic radius of atoms generally increases from top to bottom within a group.

How does atomic radius vary down the group 1 and group 2?

On moving down the group, the number of shells increases due to which the distance between the nucleus and outermost shell also increases, therefore, the atomic size of the atoms increases.

Why does atomic radius decrease across a period 2?

Atomic radius decreases across a period because valance electrons are being added to the same energy level at the same time the nucleus is increasing in protons. The increase in nuclear charge attracts the electrons more strongly, pulling them closer to the nucleus.