PHP, 507 485 476476 466 characters
Usage: enter the element name as GET parameter '0' - elements.php?0=carbon
Algorithm: Run through the data string, pulling out substring,abbreviation code pairs. If the substring matches the start of the element passed in, use the abbreviation code to determine what to output: If the code starts with a letter, output it as a string. If it is a number N, output the first letter of the element + the Nth letter. The Unun elements are special-cased with the code '|'. If no substring is found that matches the name passed in, output the first two characters of the name as the abbreviation.
Readable Code:
<?php
$l=ucfirst(strtolower($_GET[0]));
for(
$m[3]="AnSbArs2As2Berk3Boh2BoBCad2Cae3Cali4CarCChl2Ch2Cope5CopCuCu5Da4Du2Ei3Fe3FluFGad2GoAuHaf2Ha2HyHIo0IroFeLaw3LePbLiv2Mag2Man2Mei3Men3MeHgNeod3Nep2Nio3NiNOxOPa5PhPPla3Plu2PotKProm3Pro4Rado4Rhe2Roe5Rub2Ruther6Sa2Sea6SilvAgSoNaSt2SuSTec2Ter3Tha3Thu6TinSnTuWUn|UUVVYtte5YYZin2Z2";
while( preg_match('/(.[a-z]*)(.[a-z]*)(.*)/',$m[3],$m)
;)
if(strstr($l,$m[1]))
echo ($x=$m[2][0])>'@'?$x>'{'?"Uu$l[4]":$m[2]:$l[0].$l[$x],die;
echo $l[0]echo$l[0],$l[1];
?>
Condensed:
<?php
$l=ucfirst(strtolower($_GET[0]));$m[3]="AnSbArs2As2Berk3Boh2BoBCad2Cae3Cali4CarCChl2Ch2Cope5CopCuCu5Da4Du2Ei3Fe3FluFGad2GoAuHaf2Ha2HyHIo0IroFeLaw3LePbLiv2Mag2Man2Mei3Men3MeHgNeod3Nep2Nio3NiNOxOPa5PhPPla3Plu2PotKProm3Pro4Rado4Rhe2Roe5Rub2Ruther6Sa2Sea6SilvAgSoNaSt2SuSTec2Ter3Tha3Thu6TinSnTuWUn|UUVVYtte5YYZin2Z2";while;for(preg_match$m[3]="AnSbArs2As2Berk3Boh2BoBCad2Cae3Cali4CarCChl2Ch2Cope5CopCuCu5Da4Du2Ei3Fe3FluFGad2GoAuHaf2Ha2HyHIo0IroFeLaw3LePbLiv2Mag2Man2Mei3Men3MeHgNeod3Nep2Nio3NiNOxOPa5PhPPla3Plu2PotKProm3Pro4Rado4Rhe2Roe5Rub2Ruther6Sa2Sea6SilvAgSoNaSt2SuSTec2Ter3Tha3Thu6TinSnTuWUn|UUVVYtte5YYZin2Z2";preg_match('/(.[a-z]*)(.[a-z]*)(.*)/',$m[3],$m);)if(strstr($l,$m[1]))echo ($x=$m[2][0])>'@'?$x>'{'?"Uu$l[4]":$m[2]:$l[0].$l[$x],die;echo $l[0]die;echo$l[0],$l[1];?>