by Colin Cheng
 P: 10 There are many other particles having a larger nucleus than carbon-14 but they are stable. Why? Why is carbon-14 radioactive even though its nucleus is relatively small? Is that the strong force applied to carbon-14 is relatively small? If yes, why? Is the size of a nucleus proportional to the strong force?
Mentor
P: 12,037
 There are many other particles having a larger nucleus than carbon-14 but they are stable. Why?
Why not?
There is nothing special about C-14.

 Why is carbon-14 radioactive even though its nucleus is relatively small?
It would help to know your background here to see where the description can be based on.

The nucleus has many neutrons compared to its proton number. This means some neutrons have to go to very high-energetic energy levels (for quantum-mechanical reasons), and their decay to a proton (plus electron+neutrino) is favorable.
 Is that the strong force applied to carbon-14 is relatively small?
No.
 Is the size of a nucleus proportional to the strong force?
That question does not make sense, the strong force is not a number.
The volume of nuclei is roughly proportional to the number of nucleons in it.
 P: 10 About radioactivity So you mean radioactivity occurs when the number of neutrons is relatively higher than that of proton?
 P: 519 It's a bit more complicated than that. Protons and neutrons occupy energy levels in the nucleus not so dissimilar to how electrons occupy energy levels in atom. For a nucleus to decay the final sum of the energy states must be less than the the sum of the original ones. The Pauli exclusion principle may come into play and require that if a neutron decays, the resulting proton must end up in a higher energy level, so that this condition is not possible. And so the configuration is stable.
Emeritus
HW Helper
Thanks
PF Gold
P: 6,723
 Quote by Colin Cheng There are many other particles having a larger nucleus than carbon-14 but they are stable. Why? Why is carbon-14 radioactive even though its nucleus is relatively small? Is that the strong force applied to carbon-14 is relatively small? If yes, why? Is the size of a nucleus proportional to the strong force?
Don't look, but even hydrogen has a radioactive isotope (H3, also called tritium)

http://en.wikipedia.org/wiki/Tritium
Mentor
P: 12,037
 Quote by Colin Cheng So you mean radioactivity occurs when the number of neutrons is relatively higher than that of proton?
Both "too many neutrons" and "too few neutrons" lead to instability. The stable nuclei are somewhere in between, with a neutron to proton ratio of roughly 1:1 for small nuclei, slowly increasing towards ~1.5:1 for large nuclei.

The internal energy levels of the neutrons and protons lead to this, as Jilang explained.

 Related Discussions Introductory Physics Homework 11 Introductory Physics Homework 2 Introductory Physics Homework 2 Advanced Physics Homework 4 Introductory Physics Homework 8