Electronic Structure of 118 Atoms for the HP-41

Overview
 

-Given the atomic number Z , the following program displays the electronic configuration of 118 elements
  from Z = 1 ( Hydrogen )  to Z = 118 ( Ununoctium )
 

Program Listing
 

Data Registers:     R00 = Z = Atomic Number                    Registers R01 thru R19 contain the number of electrons in each atomic orbital.

                                R01 = 1s       R06 = 4s      R11 = 5p      R16 = 7s                   the atomic orbitals are sorted from the lowest energy ( 1s )
                                R02 = 2s       R07 = 3d      R12 = 6s      R17 = 5f                   to the highest energy ( 7p if  Z < 119 )
                                R03 = 2p      R08 = 4p      R13 = 4f       R18 = 6d                  For Z = 118, these 19 orbitals are filled.
                                R04 = 3s       R09 = 5s      R14 = 5d      R19 = 7p
                                R05 = 3p      R10 = 4d      R15 = 6p                                       R20 & R21: temp
Flag:  F29
Subroutines: /

-Some elements don't follow the simplest rule to fill the atomic orbitals,
  and lines 37 to 128 deal with these exceptions.
-The "append" character is denoted  ~
-Line 175 = one space.
 
 

01  LBL "ATOM"   02  STO 00   03  2   04  STO 01   05  STO 02   06  STO 04   07  STO 06   08  STO 09   09  STO 12   10  STO 16   11  6   12  STO 03   13  STO 05   14  STO 08   15  STO 11   16  STO 15   17  7   18  STO 19   19  10   20  STO 07   21  STO 10   22  STO 14   23  STO 18   24  14   25  STO 13   26  STO 17   27  119   28  RCL 00   29  -   30  19   31  LBL 01   32  DSE IND X   33  X=0?   34  DSE X   35  DSE Y   36  GTO 01   37  RCL 00   38  ST+ X    39  53   40  -   41  5

42  /   43  X^2   44  1   45  X#Y?   46  CLX   47  ST- 06   48  ST+ 07   49  RCL 00           50  46   51  /   52  1   53  X#Y?   54  CLX   55  ST- 09   56  ST+ 10   57  43   58  RCL 00   59  X=Y?   60  GTO 10   61  44   62  -   63  3   64  /   65  X^2   66  1   67  X<Y?   68  CLX   69  ST- 09   70  ST+ 10   71  RCL 00   72  58   73  X=Y?   74  GTO 02   75  DSE X   76  X=Y?   77  GTO 02   78  7   79  +   80  X#Y?   81  GTO 03   82  LBL 02

83  SIGN   84  ST- 13   85  ST+ 14   86  LBL 03   87  RCL 00           88  ST+ X   89  157   90  -   91  X^2   92  1   93  X#Y?   94  CLX   95  ST- 12   96  ST+ 14   97  RCL 00   98  91   99  - 100  2 101  / 102  X^2 103  1 104  X<Y? 105  CLX 106  ST- 17 107  ST+ 18 108  RCL 00 109  93 110  - 111  3 112  / 113  X^2 114  1 115  X#Y? 116  CLX 117  ST- 17 118  ST+ 18 119  RCL 00 120  ST+ X 121  221 122  - 123  X^2

124  1 125  X#Y? 126  CLX 127  ST- 16 128  ST+ 18 129  LBL 10 130  CLX 131  STO 20         132  FIX 0 133  CF 29 134  RCL 01 135  XEQ 02 136  CLST 137  RCL 03 138  RCL 02 139  XEQ 02 140  CLST 141  RCL 07 142  RCL 05 143  RCL 04 144  XEQ 02 145  RCL 13 146  RCL 10 147  RCL 08 148  RCL 06 149  XEQ 02 150  RCL 17 151  RCL 14 152  RCL 11 153  RCL 09 154  XEQ 02 155  CLST 156  RCL 18 157  RCL 15 158  RCL 12 159  XEQ 02 160  CLST 161  RCL 19 162  RCL 16 163  XEQ 02 164  GTO 03

165  LBL 02 166  X=0? 167  RTN 168  XEQ 02 169  AVIEW 170  COS 171  COS 172  COS 173  RTN 174  LBL 02 175  " " 176  ISG 20          177  CLX 178  ARCL 20 179  ASTO 21 180  "~S" 181  ARCL X 182  RDN 183  X=0? 184  RTN 185  ARCL 21 186  "~P" 187  ARCL X 188  RDN 189  X=0? 190  RTN 191  ARCL 21 192  "~D" 193  ARCL X 194  RDN 195  X=0? 196  RTN 197  ARCL 21 198  "~F" 199  ARCL X 200  RTN 201  LBL 03 202  FIX 4 203  SF 29 204  CLA 205  END

 
    ( 307 bytes / SIZE 022 )
 
 

STACK	INPUT	OUTPUT
X	Z = atomic number	/

     ( with  0 < Z < 119 )

 
Examples:     Z = 43 ( Technetium )   ,   Z = 78  ( Platinium )

   43  XEQ "ATOM"  and  the HP-41 displays:

        1S2
        2S2 2P6
        3S2 3P6 3D10
        4S2 4P6 4D5
        5S2

-The electronic structure is usually denoted:    1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d⁵5s²

     78    R/S   yields

            1S2
            2S2 2P6
            3S2 3P6 3D10
            4S2 4P6 4D10 4F14
            5S2 5P6 5D9
            6S1

-And the electronic structure is:   1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰4f¹⁴5s²5p⁶5d⁹6s¹

Notes:

-Execution times vary between 6 seconds ( for Z = 118 ) to 30 seconds ( for Z = 1 )
-The structure is displayed layer after layer.
-Lines 170-171-172 are only useful to slow down execution between 2 AVIEWs
-Press XEQ 10 to display the configuration again.
-Set flag F21 if you want to stop the calculator at each AVIEW

-For Z = 58 ( Cerium ) this program yields    1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰4f¹5s²5p⁶5d¹6s²          both configurations have
          but another source gives                        1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰4f²5s²5p⁶6s²                almost the same energy!

-If you prefer the second structure, replace lines  71 thru 86  by

  RCL 00   ST+ X   121   -   7   /   X^2   1   X#Y?   CLX   ST- 13   ST+ 14

-For  Z = 111 ( Roentgenium ),
           this program gives                  1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰4f¹⁴5s²5p⁶5d¹⁰5f¹⁴6s²6p⁶6d¹⁰7s¹     ( it seems to be the most probable structure )
           but it could be also                 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰4f¹⁴5s²5p⁶5d¹⁰5f¹⁴6s²6p⁶6d⁹7s²

-If you want to get this output, replace lines 119 thru 123  by  RCL 00   110   /
 
 

Reference:

[1]  "Periodic Table of the Elements" - Los Alamos National Laboratory -  cf   www.lanl.gov