Why are technetium (atomic no. 43) and promethium (61) alone among the
elements of atomic number less than 84 (whoops - got this wrong last
time) in having no stable isotopes?
Do they have an 'unstable' number of protons in their nuclei?

It is a similar reason to periodic table of element:
Nucleus with 'closed shell' of nucleons is more stable,
corresponding to 'noble gas' elements.

 explanation of how neutrons and protons within atomic nuclei are structured.
Called the "nuclear shell model," her work explains why the nuclei of some
atoms are more stable than others and why some elements have many different
atomic forms, called "isotopes," while others do not. For this work, she
shared the 1963 Nobel Prize in physics
http://www.osti.gov/accomplishments/mayer.html


More technical details ( jj-coupling shell model) 
http://www2.kutl.kyushu-u.ac.jp/seminar/MicroWorld3_E/3Part2_E/3P26_E/shell_m
odel_E.htm

Still more technica
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html#c3

Search Terms: magic numbers, shell model, nucleus