Nucleus
Robert Deaton Spring 2022
Discovery of the Nucleus
If we hearken back to the days of the turn of the 20th century (a truly revolutionary time in physics history), we have to consider the plum-pudding model of an atom put forth by J. J. Thompson just a few years ago in 1904. Thomson had discovered the electron in 1897, and to account for the neutral charge of regular matter and the negative charge of electrons, he proposed that atoms were made of some positively charged *stuff* (pudding) with negatively charged electrons embedded inside (plums). Over the next several years, many experiments headed by Ernest Rutherford and Hans Geiger showed that alpha particles emitted by radioactive elements move more slowly through solid matter than through air (testing with aluminium foil and gold leaf).
So something crazy wild happened in 1909 when Rutherford began paying attention to the trajectories followed by the alpha particles when shot at gold leaf. According to the plum pudding model, the positively charged stuff of the atom should have a negligible effect on the alpha particles because it is evenly distributed. Likewise, the electrons shouldn't affect the trajectory of the particles because their mass is so much smaller; they would just be flung away. So it came as a surprise to Rutherford (and physicists everywhere!) when a substantial number of alpha particles were deflected by significant amounts (several degrees even), and many went in all sorts of directions, including backwards! See the image for a better description.
Rutherford's experiment showed that the center of an atom contained all of an atom's positive charge and mass, and within a couple years, physicists had updated their conceptual model of atoms to account for this. Rutherford had proven that hydrogen nuclei were present in other nuclei and, with the discovery of isotopes (due to physics' newfound fascination with radioactivity), a new atomic hypothesis was formed: the nuclear electrons hypothesis. Since atomic masses are roughly in multiples of the hydrogen nuclei, and hydrogen nuclei were present in other nuclei, it was proposed that protons (hydrogen nuclei) make up the mass of nuclei and electrons are "embedded" in it to balance the charge. For example, in nitrogen-14, there would be 14 protons and 7 electrons in the nucleus to make a net charge of +7. However, there were several issues with the embedded electrons hypothesis. For one, it would cause additional spectral line splitting (at a very fine level) that was not actually observed, and it would cause some nuclei to have a net spin inconsistent with measured values.
Then, in 1932,
A Mathematical Model
Some helpful numbers, definitions, and mathematical concepts to know: protons: carry positive charge around nuclei, symbol: p
neutrons: no electric charge, relatively same mass as proton, symbol: n
electron: negatively charged, symbol: e
atomic number= number of protons, helps us define the chemical properties of an element so we can arrange it on the periodic table
mass number= number of protons + neutrons, this number can change slightly if the number of neutrons changes --> making an isotope
isotope: types of atoms that have the same number of protons and position in periodic table but a different number of neutrons
mass of a proton= 1.673x10^-27 kg, charge of proton: 1.6x10^-19 coulomb
mass of an electron= 9.109x10-31 kg, charge of electron = - 1.6x10^-19 coulomb