Atomic Radius:

(1)     The radius of an atom may be taken as the distance between atomic nucleus and the outermost shell of electrons of the atom.

(2)     According to the Heisenberg’s uncertainty principle the position of a moving electron cannot be accurately determined. So the distance between the nucleus and the outermost electron is uncertain.

(3)     Atomic radius can be determined indirectly from inter nuclear distance between the two atoms in a gaseous diatomic molecule. This internuclear distance between the two atoms is called bond length.

(4)     The internuclear distance between the two atoms can be measured by X– ray diffraction or spectroscopic studies and also nuclear magnetic resonance (NMR) spectrum.

(5)     Atomic radius depends on the type of chemical bond between atoms in a molecule. These are:

(i)   Covalent radius

(ii) Metallic radius or crystal radius

(iii) Vander Waal’s radius

(iv) Ionic radius or Collision radius

(6) Periodicity in Atomic Radius and Ionic Radius: 

Related Questions:

(1) What are the Amphoteric metals ? gives Examples.

(2) Name of total metalloids present in periodic table ?

(3) Total numbers of elements which are liquid at normal temperature is ?

(4) What is Mendeleev's periodic table ? give important features and draw back of Mendeleev's table.

(5) What is atomic density ? give the periodicity of atomic density in periods and groups.

(6) What is atomic volume ? and what is periodicity of atomic volume in groups and periods ?

(7) Why there are 2, 8 and 8 elements in first, second and third periodic of periods table respectively ? Explain.

(8) In alkali metal group which is the strongest reducing agent in aqueous solution and why?

(9) The electron affinity of sulphur is greater than oxygen. Why?

(10) The first ionization energy of carbon atom is greater than that of boron atom, whereas reverse is true for the second ionization energy. Explain.

(11) The electronegativities of B, Al, Ga are 2.0, 1.5, 1.6 respectively. The trend is not regular. Explain.

(12) Li2CO3 decomposes on heating but other alkali metal carbonates don’t. Explain.

(13) Of all noble metals, gold has got a relatively high electron affinity. Explain.

(14) What are the increasing order of ioni radii of first group elements in water ?

(15) What are the increasing order of molar conductivity of first group elements in water ?

Covalent radius:

Covalent radius: It is defined as one half of the distance between the nuclei (inter nuclear distance) of two covalently bonded like atoms in a homo nuclear diatomic molecule is called the covalent radius of that.

(A) For Homo atomic Molecules: The covalent radius (r_A) of atom A in a molecule A₂ may be given as:

The distance between nuclei of two single covalently bonded atoms in homo diatomic molecules is equal to the sum of covalent radii of both the atoms.

Illustrative example (1): A given compound A₂ whose total d_A-A is 1.4 A⁰. The atomic (covalent) radius of an atom is.

Solution:  We known that

(B) For Heteroatomic Molecules: In a hetero diatomic molecules AB where the electro negativity of atoms A and B are different, the experimental values of inter nuclear distance d_A-B is less than the theoretical value (r_A +r_B).

(1) Stevenson & Schoemaker Equation (1941):

Covalent radius of heterogeneous molecule like A-B etc determine by Stevenson & Schromaker Equation, if atoms are formed different type of covalent bond i.e. on atom is more electronegative than the other combined atom. Then the covalent radius is calculated by the relation given by Stevenson & Schoemaker, given as:

For a diatomic Hetero molecule:

Bond Length (l_A-B) = r_A + r_B- 0.09(X_A-X_B)

Where X_A= Electronegativity of more electronegative atom

Where X_B= Electronegativity of less electronegative atom

Illustrative examples 

(1) The electronegativity of F and H are 4.0 and 2.1 respectively. The percentage ionic character in H and F bond is.

(2) A given compound A2 whose total dA-A is 1.4 A0. The atomic (covalent) radius of an atom is.

(3) A given compound AB whose electronegative difference is 1.9 . Atomic radius of A and B are 4 and 2 Angstroms the distance between A and B means dA-B is ?

(4)If covalent radius of A is 0.99 A0 and bond length is 1.46 A0 Calculate the covalent radius of B. XA and XB are 3.5 and 2.5 respectively.

(5) The C–C single bond length is 1.54 Angstroms and that of Cl–Cl is 1.98 Angstroms. If the electronegativity of Cl and C are 3.0 and 2.5 respectively, the C–Cl bond-length will be equal to ?

(2) Puling equation: If the electro negativities of the two atoms A and B are X_A and X_B   respectively then

                    Bond Length (d_A-B) =( r_A +r_B)-(C₁X_A-C₂X_B)

Where C₁ and C₂ are the Stevenson’s coefficients for atoms A and B respectively 

Related Questions:

(1) What are the Amphoteric metals ? gives Examples.

(2) Name of total metalloids present in periodic table ?

(3) Total numbers of elements which are liquid at normal temperature is ?

(4) What is Mendeleev's periodic table ? give important features and draw back of Mendeleev's table.

(5) What is atomic density ? give the periodicity of atomic density in periods and groups.

(6) What is atomic volume ? and what is periodicity of atomic volume in groups and periods ?

(7) Why there are 2, 8 and 8 elements in first, second and third periodic of periods table respectively ? Explain.

(8) In alkali metal group which is the strongest reducing agent in aqueous solution and why?

(9) The electron affinity of sulphur is greater than oxygen. Why?

(10) The first ionization energy of carbon atom is greater than that of boron atom, whereas reverse is true for the second ionization energy. Explain.

(11) The electronegativities of B, Al, Ga are 2.0, 1.5, 1.6 respectively. The trend is not regular. Explain.

(12) Li2CO3 decomposes on heating but other alkali metal carbonates don’t. Explain.

(13) Of all noble metals, gold has got a relatively high electron affinity. Explain.

(14) What are the increasing order of ioni radii of first group elements in water ?

(15) What are the increasing order of molar conductivity of first group elements in water ?

Why Back bonding does not take place in P(SiH3)3 instead of phosphorus has lone pair and Silicon has vacant d-orbital but in N(SiH3)3 molecule back bonding does take place?

Conditions for back bonding:

(1) Both of the atoms bonded with back Bonding are must be present in 2nd-2nd or 2nd-3rd period. 4rth period onward back bonding does not take place.

(2) One of the atoms has lone pair (donor atom) and another (acceptor atom) have vacant Orbital and direction of back Bonding depends upon vacant Orbital.

(3) The donor atom must have localized donatable electron pair and there should be inter electronic repulsion (smaller size). In general these are later half second period P - block elements (F, O, N and C).

(4) The acceptor atom must have low energy empty orbital which generally are np or nd orbitals. Small and similar size orbital’s favour overlap.

(5) Back bonding is a weak pi bond thus only effective overlapping will be form back bonding.

(6) Back bonding is found to be effective and considerable in following type of overlapping.

 (i) 2p-2p

(ii) 2p-3p

(iii) 2p-3d 

(7) The extent of overlapping order is [2p-2p> 2p-3d >2p-3p]

(8) dx²-y² and dx² Orbital’s does not participate in back Bonding. 

Solution:

In case of  trisilyl phosphine [P(SiH₃)₃]  Phosphorous (P) being larger in atomic size so it does not face much interelectronic repulsion and so, not much eager to donate it’s loan pair electron and comfortable with it. So, it will not donate to Si atom in this case. Thus, back bonding will not take place in trisilyl phosphine [P(SiCH₃)₃].

But in the case of trisilyl amine [N(SiH₃)₃], the nitrogen (N) atom is smaller in atomic size leading to high interelectronic repulsion, so it wants ease by donating it’s loan pair electron to other atoms near to it. And Si has vacant d-orbital, so needy for it. Since both conditions are follow here,  hence back bonding will take place.

 Related Questions:

(1) Why trimethylamine amine ( N(CH3)3) is tetrahedral while trisilyl amine (N(SiH3)3) planner.?

(2) Why trimethyl amine {(CH3)3 N:} is pyramidal while trisilyl amine {(SiH3)3N:} is trigonal planer?

(3) Which is/are the correct statement/s about structure of methyl isothiocyanate (H3CNCS) and Silyl isothiocyanate(SiH3NCO)?

(4) What is the Si–N–C bond angle in Silyl isothiocyanate and methyl isothiocyanate (H3CNCS)?

(5) What are the order of extent back bonding, Lewis acid character and nucleophilicity of (BF3, BCl3, BBr3, BI3)boron trihalides?

(6) Arrange the silicon halides into decreasing order of Lewis acids Character? SiF4, SiCl4, SiBr4, SiI4

(7) Which of the following correct statement about structure of Ortho boric acid (H3BO3 ) is/are? Statements are as

(8) Which of the following is correct order of (B-O) bond length of following compounds? (1) B(OH)3 (2) B(OMe)3 and (3) B(Me)2OH

(9) What are the structure of (1) N(SiH3)3 (2) {(Me)3Si}2N-Si(Me)3 (3) HN(SiH3)2 and give the Answers of following questions?

Metallic radius or Crystal radius:

Metallic radius or Crystal radius:

(1) The term crystal radius is used to denote the size of atoms in metal.

(2) Metal atoms are closely packed spheres in metallic crystal. The metal atoms are supposed to touch one another in crystal.

(3) Metallic radius is defined as one half the distances between the centres of the nuclei of two atoms in a metallic crystal.

(4) Metallic radius is determined by X-ray diffraction method.

(5) Metallic radii are about 10 to 15 % higher than the single bond covalent raddi of those elements. Thus single bond covalent radius is smaller than the metallic radius due to the no overlapping of atomic orbital in metallic bond.

Vander Waal’s radius > Metallic radius > Covalent radius

(6) For the simplicity the term atomic radius is used for covalent radius as well as metallic radius depending on whether the element is a non-metal or metal. However, the atomic radii of inert gases are expressed in the terms of Vander Waal’s radii.

(7) Metallic radius is inversely proportional to the metallic bond strength.

(8) More metallic radius –loose crystal packing-less bond strength. (BCC)

(9) Less metallic radius –Tight crystal packing (FCC) - high bond strength.(HCP)

(10) For non-metal, atomic radius means covalent radius.

(11) For metal, atomic radius means metallic radius.

(12) For inert gases, atomic radius means Vander Waal’s radius.

Vander Waal’s radius or Collision radius:

Related Questions:

(1) What are the Amphoteric metals ? gives Examples.

(2) Name of total metalloids present in periodic table ?

(3) Total numbers of elements which are liquid at normal temperature is ?

(4) What is Mendeleev's periodic table ? give important features and draw back of Mendeleev's table.

(5) What is atomic volume ? and what is periodicity of atomic volume in groups and periods ?

(6) Why there are 2, 8 and 8 elements in first, second and third periodic of periods table respectively ? Explain.

(7) In alkali metal group which is the strongest reducing agent in aqueous solution and why?

(8) The electron affinity of sulphur is greater than oxygen. Why?

(9) The first ionization energy of carbon atom is greater than that of boron atom, whereas reverse is true for the second ionization energy. Explain.

(10) The electronegativities of B, Al, Ga are 2.0, 1.5, 1.6 respectively. The trend is not regular. Explain.

(11) Li2CO3 decomposes on heating but other alkali metal carbonates don’t. Explain.

(12) Of all noble metals, gold has got a relatively high electron affinity. Explain.

(13) Ionization energy of Boron is smaller than Beryllium even though effective nuclear charge is higher?

(14) What are the increasing order of ioni radii of first group elements in water ?

(15) What are the increasing order of molar conductivity of first group elements in water ?

What is the shielding constant (S) experienced by a 3d electron in the bromine atom?

Step (1): Write the electronic configuration of Bromine in the appropriate form.

Br: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵

Br: (1s²)(2s²,2p⁶)(3s²,3p⁶)(3d¹⁰)(4s²,4p⁵)

Step (2): Use the Slater Rule to calculate the shielding constant for the electron. And ignore the group of electron to the right of the 3d electrons, these electrons do not contribute to the shielding constant.

(S)_3d = (d electrons-1)x 0.35+ (remaining electrons)x1.00= 21.15

(S)_3d = (10-1)x 0.35+ (18)x1.00= 21.15

Solved Questions:

(2) A given compound AB whose electronegative difference is 1.9 . Atomic radius of A and B are 4 and 2 Angstroms the distance between A and B means dA-B is ?

(2) The C–C single bond length is 1.54 Angstroms and that of Cl–Cl is 1.98 Angstroms. If the electronegativity of Cl and C are 3.0 and 2.5 respectively, the C–Cl bond-length will be equal to ?

(3) Stevenson & Schromaker Equation: Determination covalent radius of Heterogeneous Molecules.

(4) How to calculate percentage (%) ionic character in covalent compounds?

(5) The electronegativity of F and H are 4.0 and 2.1 respectively. The percentage ionic character in H and F bond is.

Related Questions:

(1) What are the Amphoteric metals ? gives Examples.

(2) Name of total metalloids present in periodic table ?

(3) Total numbers of elements which are liquid at normal temperature is ?

(4) What is Mendeleev's periodic table ? give important features and draw back of Mendeleev's table.

(5) What is atomic density ? give the periodicity of atomic density in periods and groups.

(6) What is atomic volume ? and what is periodicity of atomic volume in groups and periods ?

(7) Why there are 2, 8 and 8 elements in first, second and third periodic of periods table respectively ? Explain.

(8) In alkali metal group which is the strongest reducing agent in aqueous solution and why?

(9) The electron affinity of sulphur is greater than oxygen. Why?

(10) The first ionization energy of carbon atom is greater than that of boron atom, whereas reverse is true for the second ionization energy. Explain.