© Copyright 1995, R.Lanigan-O'Keeffe, Sydney Australia. Not for copying without permission.

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Appendix Five

Atomic Radii

Two distinct molecular structures are observed through measurement techniques such as X-ray diffraction. These have been given the banner names of Ionic and Covalent atomic radii. There are considerable differences between the two. The measurements of the radii is expressed in Angstroms, 1Å = 10-10. To determine the bond length of a covalent molecule, the covalent radii of the molecular parts is added. Likewise, the Ionic bond length is determined by adding the respective Ionic radii together. Although these measurements refer to distances, the relationship between the calculated geometric radii and the particular radii indicate the molecular forces involved. The belief is that the atomic radii decreases from the left side of the periodic table to the right side as atomic mass increases. This assertion of fact is not "always" true, as seen across every period from K to RN. Ask the question "What do these listing actually reveal?"

COVALENT RADII Å
















H
0.3		 He
---










Li
1.33		Be
0.89		B
0.8		C
0.77		N
0.74		O
0.74		F
0.72		Ne
---










Na
1.57		Mg
1.36		Al
1.25		Si
1.17		P
1.1		S
1.04		Cl
0.99		Ar
---
K
2.03		Ca
1.74		Sc
1.44		Ti
1.32		V
1.22		Cr
1.17		Mn
1.17		Fe
1.16		Co
1.16		Ni
1.15		Cu
1.17		Zn
1.25		Ga
1.25		Ge
1.22		As
1.21		Se
1.17		Br
1.14		Kr
---
Rb
2.16		Sr
1.91		Y
1.61		Zr
1.45		Nb
1.34		Mo
1.29		Tc
---		Ru
1.24		Rh
1.25		Pd
1.28		Ag
1.34		Cd
1.41		In
1.50		 Sn
1.41		Sb
1.41		Te
1.37		I
1.33		Xe
---
Cs
2.35		Ba
1.98		La
1.69		Hf
1.44		Ta
1.34		W
1.30		Re
1.28		Os
1.26		Ir
1.26		Pt
1.29		Au
1.34		Hg
1.44		Tl
1.55		Pb
1.54		Bi
1.52		Po
1.52		At
---		Rn
---

Ce
1.65		Pr
1.65		Nd
1.64		Pm
---		Sm
1.66		Eu
1.85		Gd
1.61		Tb
1.59		Dy
1.59		Ho
1.58		Er
1.57		Tm
1.56		Yb
1.70		Lu
1.56

---------------------

IONIC RADII Å

















H
1.45		 He
---










Li
0.78		Be
0.31		B
0.2		C
---		N
---		O
1.4		F
1.36		Ne
---










Na
0.98		Mg
0.65		Al
0.50		Si
0.43		P
---		S
1.84		Cl
1.81		Ar
---
K
1.33		Ca
0.99		Sc
0.81		Ti
0.68		V
---		Cr
---		Mn
---		Fe
0.60		Co
---		Ni
---		Cu
0.96		Zn
0.74		Ga
0.62		Ge
0.53		As
---		 Se
1.98		Br
1.95		Kr
---
Rb
1.48		Sr
1.13		Y
0.93		Zr
0.74		Nb
---		Mo
---		Tc
---		Ru
---		Rh
---		Pd
1.28		Ag
1.26		Cd
0.97		In
0.81		 Sn
0.71		Sb
---		Te
2.21		I
2.16		Xe
---
Cs
1.69		Ba
1.35		La
1.22		Hf
---		Ta
---		W
---		Re
---		Os
---		Ir
---		Pt
1.29		Au
1.37		Hg
1.10		Tl
0.95		Pb
0.84		Bi
---		Po
---		At
---		Rn
---


m3+

Ce
1.01
1.06		Pr
---		Nd
---		Pm
---		Sm
---		Eu
---		Gd
---		Tb
---		Dy
---		Ho
---		Er
---		Tm
---		Yb
---		Lu
1.56
0.85

The Lanthanide Contraction falls from La at 1.69 to Lu at 1.56 Å, and for the m3+ ions from 1.06 to 0.85. The value for the m3+ ion of La is stated in the above table as 1.22 and from the reference text "Inorganic Chemistry" by Heslop and Robinson, to also have an m3+ ion measuring 1.06 Å at the same time. A blatant contradiction, perhaps an error, but accepted by educators and students as the facts.

COVALENT AND IONIC RADII

















H
0.3
1.45		 He
---










Li
1.33
0.78		Be
0.89
0.31		B
0.8
0.20		C
0.77
---		N
0.74
---		O
0.74
1.40		F
0.72
1.36		Ne
---










Na
1.57
0.98		Mg
1.36
0.65		Al
1.25
0.50		Si
1.17
0.43		P
1.1
---		S
1.04
1.84		Cl
0.99
1.81		Ar
---
K
2.03
1.33		Ca
1.74
0.99		Sc
1.44
0.81		Ti
1.32
0.68		V
1.22
---		Cr
1.17
---		Mn
1.17
---		Fe
1.16
0.60		Co
1.16
---		Ni
1.15
---		Cu
1.17
0.96		Zn
1.25
0.74		Ga
1.25
0.62		Ge
1.22
0.53		As
1.21
---		Se
1.17
1.98		Br
1.14
1.95		Kr
---
Rb
2.16
1.48		Sr
1.91
1.13		Y
1.61
0.93		Zr
1.45
0.74		Nb
1.34
---		Mo
1.29
---		Tc
---		Ru
1.24
---		Rh
1.25
---		Pd
1.28
1.28		Ag
1.34
1.26		Cd
1.41
0.97		In
1.50
0.81		 Sn
1.41
0.71		Sb
1.41
---		Te
1.37
2.21		I
1.33
2.16		Xe
---
Cs
2.35
1.69		Ba
1.98
1.35		La
1.69
1.22		Hf
1.44
---		Ta
1.34
---		W
1.30
---		Re
1.28
---		Os
1.26
---		Ir
1.26
---		Pt
1.29
1.29		Au
1.34
1.37		Hg
1.44
1.10		Tl
1.55
0.95		Pb
1.54
0.84		 Bi
1.52
---		Po
1.52
---		At
---		Rn
---




m3+

Ce
1.65
1.01
1.06		Pr
1.65
---		Nd
1.64
---		Pm
---		Sm
1.66
---		Eu
1.85
---		Gd
1.61
---		Tb
1.59
---		Dy
1.59
---		Ho
1.58
---		Er
1.57
---		Tm
1.56
---		Yb
1.70
---		Lu
1.56
1.56
0.85

-----------------------------

COVALENT, IONIC and CALCULATED (from the amu) RADII
















H
0.3
1.45
0.6		 He
---
---
0.78159










Li
1.33
0.78
1.186		Be
0.89
0.31
1.29		B
0.8
0.20
1.379		C
0.77
---
1.42		N
0.74
---
1.495		O
0.74
1.40
1.563		F
0.72
1.36
1.655		Ne
---
---
1.684










Na
1.57
0.98
1.764		Mg
1.36
0.65
1.789		Al
1.25
0.50
1.861		Si
1.17
0.43
1.884		P
1.1
---
1.948		S
1.04
1.84
1.969		Cl
0.99
1.81
2.04		Ar
---
---
2.121
K
2.03
1.33
2.103		Ca
1.74
0.99
2.12		Sc
1.44
0.81
2.206		Ti
1.32
0.68
2.254		V
1.22
---
2.3		Cr
1.17
---
2.315		Mn
1.17
---
2.359		Fe
1.16
0.60
2.37		Co
1.16
---
2.415		Ni
1.15
---
2.415		Cu
1.17
0.96
2.47		 Zn
1.25
0.74
2.506		Ga
1.25
0.62
2.544		Ge
1.22
0.53
2.59		As
1.21
---
2.62		Se
1.17
1.98
2.66		Br
1.14
1.95
2.673		Kr
---
---
2.716
Rb
2.16
1.48
2.738		Sr
1.91
1.13
2.76		Y
1.61
0.93
2.769		Zr
1.45
0.74
2.79		Nb
1.34
---
2.81		Mo
1.29
---
2.84		Tc
---
---
2.86		Ru
1.24
---
2.888		Rh
1.25
---
2.907		Pd
1.28
1.28
2.94		Ag
1.34
1.26
2.96		Cd
1.41
0.97
2.99		In
1.50
0.81
3.016		 Sn
1.41
0.71
3.05		Sb
1.41
---
3.08		Te
1.37
2.21
3.12		I
1.33
2.16
3.11		Xe
---
---
3.15
Cs
2.35
1.69
3.166		Ba
1.98
1.35
3.19		La
1.69
1.22
3.123		Hf
1.44
---
3.489		Ta
1.34
---
3.51		W
1.30
---
3.53		Re
1.28
---
3.54		Os
1.26
---
3.56		Ir
1.26
---
3.57		Pt
1.29
1.29
3.59		Au
1.34
1.37
3.61		Hg
1.44
1.10
3.627		Tl
1.55
0.95
3.65		Pb
1.54
0.84
3.67		 Bi
1.52
---
3.68		Po
1.52
---
3.69		At
---
---
3.69		Rn
---
---
3.75




m3+

Ce
1.65
1.01
1.06
3.22		Pr
1.65
---
---
3.22		Nd
1.64
---
---
3.26		Pm
---
---
---
3.26		Sm
1.66
---
---
3.29		Eu
1.85
---
---
3.13		Gd
1.61
---
---
3.34		Tb
1.59
---
---
3.38		Dy
1.59
---
---
3.38		Ho
1.58
---
---
3.40		Er
1.57
---
---
3.416		Tm
1.56
---
---
3.429		Yb
1.70
---
---
3.456		Lu
1.56
1.56
0.85
3.469

The following basic program can be used to determine the calculated diameters from the published accepted atomic mass units (amu). This simple program determines the value of r3 from the known accepted mass, and calculates the cube root of r3 from 1 to 500. As a check, when it prints to the screen, it also calculates the volume in the third column, as determined from the spherical equation

V = (4/3) r3

The mathematical routines of various computer systems will be of concern, since some basic languages cannot handle simple mathematics. The hash symbol may introduce floating point mathematics into the operation depending on the language. The values returned for Helium should be:-

4 mass
0.9847450212668305 radius
4.00000010762118 volume

PROG: ATOM .BAS

  • 5 P#=3!/(4!*3.14159265):s#=0.5
  • 10 FOR I#=1 TO 500:R3#=P#*I#
  • 20 GOTO 50
  • 30 NEXT I#
  • 35 STOP:END
  • 50 B#=0.01:GOSUB 70
  • 51 B#=0.001:GOSUB 70
  • 52 B#=0.0001:GOSUB 70
  • 53 B#=0.00001:GOSUB 70
  • 54 B#=0.000001:GOSUB 70
  • 55 B#=0.0000001:GOSUB 70
  • 56 B#=0.00000001:GOSUB 70
  • 57 B#=0.000000001:GOSUB 70
  • 58 V#= (4/3)*3.14159265*(R#^3)
  • 60 PRINT I#, R#, V# : GOTO 30
  • 65 STOP:END
  • 70 FOR S#=A# TO I# STEP B#
  • 71 G#=S#^3
  • 72 IF G#>R3# THEN S#=S#-B#:A#=S#:R#=A#:RETURN
  • 73 NEXT S#:RETURN
  • 75 STOP :END

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