The discovery of nuclear fission was originally explained by modeling the atomic nucleus as a drop of liquid. Like a water balloon, the drop could spin or vibrate, and if the motion became
sufficiently violent, the drop could split in half — undergo fission. It was later learned that even the nuclei in matter under ordinary conditions are often not spherical but deformed,
typically with an elongated ellipsoidal shape like an American football. One simple way of describing such a shape is with the equation ![r\leq b[1+c(cos^{2}\theta -k)],](/system/files/resource/33/33298/34316/media/eqn-img_2.gif)
where c= 0 for a sphere, c>0 for an elongated shape, and
c<0 for a flattened one. Usually for nuclei in ordinary matter, cranges from about 0 to +0.2. The constant k is introduced because without it, a change in
cwould entail not just a change in the shape of the nucleus, but a change in its volume as well. Observations show, on the contrary, that the nuclear fluid is highly incompressible,
just like ordinary water, so the volume of the nucleus is not expected to change significantly, even in violent processes like fission. Calculate the volume of the nucleus, throwing away terms
of order 
or higher, and show that k= 1/3 is
required in order to keep the volume constant.
- 1008 reads
