Why some nuclei are stable, other not, it is not fully understood yet. It is known that isotopes with even number of protons and neutrons are more stable, and the most unstable are with uneven numbers of protons and neutrons. So, the biggest energy of the bound has a small nucleus of helium 2+2 (₂⁴He), and also "intermediate" nuclei, like iron (₂₆⁵⁶Fe). It is also known that nuclei are similar do droplets, but not totally free in shape; neither they are arrangement of orbits like atoms.

Oxygen (Z=8), calcium (Z=20), nickel (Z=28), tin (Z=50) and lead (Z=82) have "magical" numers of protons and due to that fact they have quite big number of stable isotopes*). Also Z=114 should be a magic number. Race is continued, who first gets to the "island od stability".

To the island, from the known land (Z=94) is still far. In Darmstadt (Germany) there is a strategy of "riveting" of two similar nuclei: in that way they obtained bohrium (Z=107), hassium (108), meitnerium (109) and new elements without names with Z=110 ***), 111 i 112. Unfortunately Z=112 lives only for  280 mikroseconds.

In Dubna (Russia) they shot calcium (⁴⁸Ca) into plutonium ²⁴⁴Pu. It seems that Z=114 lives till 30 seconds!

*) For example, stable isotopes of oxygen are:
¹⁶O (on Earth - relative to other isotopes 99,762% ), ¹⁷O (0,038%), ¹⁸O (0,20%)**),
in comparison with an unstable ones:
¹³O (t=9 ms), ¹⁴O (t=71 s), ¹⁵O (t=122 s), ¹⁹O (t=27 s), ²⁰O (t=13 ms), ²¹O (t=3.14 s),
amonf seven isotopes of fluorium only one is stable.
Lead has 4 stable isotopes - from 32 possible (from A=184 to A=214).
**) That isotope has a fundamental importance in paleoclimatology. Water containing that isotope is heavier. Because processes of evaporation are more intensive near the equator than on higher latitudes, "heavy" water has less chances to get to poles - arctic ice contains less of that isotope than "normal" water. When ice is melting, oceans get poorer in that isotope and there is less of it for example in shellfish. Now it is enough to examine depositions of the limestones to know how climat changed.
***) This element in 16.08.2003 during IUPAC session in w Ottawa was named darmstadtium (Ds).