Size Of The Nucleus (Math Help)

A nucleus is made up of positively charged protons and neutral (no charge) neutrons, which are collectively called nucleons. The nucleons are made up of quarks, and have a radius of about 0.8 fm (fm stands for femto meters, since femto is the metric prefix meaning 10-15, sometimes written 10^{-15} when superscripts are not available in plain text).

There is a very strong and very short-range force that pulls nucleons toward each other, and an even stronger repulsive force that keeps them from overlapping each other. The result is that a nucleus 'looks' likes a closely packed set of spheres that are almost touching one another.

Nucleus of Lithium-7

As an example, we show a schematic picture of the nucleus of Lithium-7. This nucleus has 3 protons (which gives the nucleus a charge of +3, identifying it as the element Lithium) and 4 neutrons (giving it a total mass number of 7).

Natural Lithium is made up of two isotopes: Lithium-7 (92.5%) and Lithium-6 (7.5%). Lithium-6 has 3 protons (as it must if it is to be the element Lithium) but only 3 neutrons, so it has a mass number of 6.

The atoms of these two isotopes behave almost exactly the same way when doing chemistry, since the atomic electrons only care about the charge of the nucleus, but the physical properties of these two nuclei are very different. For example, the nucleus of Lithium-7 is not spherical, as the diagram above suggests, but deformed into a football-like shape as shown below.

The nucleus does not really have a sharp surface like this picture suggests. The protons and neutrons move around and there is a fuzzy quantum-mechanical probability of finding them outside the region shown with a shiny surface. We made this picture to show where th nucleons will be found most (more than 90%) of the time.

Quark Content of Lithium-7

If we look more closely, we will notice that the protons and neutrons (nucleons) are made up of quarks interacting via gluon exchange. This is shown schematically in the picture below. Nuclear physicists can do experiments that look inside the nucleus to see the protons and neutrons, and they can also do experiments that allow them to see the role of quarks and gluons in nuclei.

Orna Cohen-Fix It is not known how the volume of the cell nucleus is set, nor how the ratio of nuclear volume to cell volume (N/C) is determined. Here, we have measured the size of the nucleus in growing cells of the budding yeast S. cerevisiae. Analysis of mutant yeast strains spanning a range of cell sizes revealed that the ratio of average nuclear volume to average cell volume was quite consistent, with nuclear volume being approximately 7% that of cell volume. At the single cell level, nuclear and cell size were strongly correlated in growing wild-type cells, as determined by three different microscopic approaches. Even in G1 phase, nuclear volume grew, although it did not grow quite as fast as overall cell volume. DNA content did not appear to have any immediate, direct influence on nuclear size, in that nuclear size did not increase sharply during S-phase. The maintenance of nuclear size did not require continuous growth or ribosome biogenesis, as starvation and rapamycin treatment had little immediate impact on nuclear size. Blocking the nuclear export of new ribosomal subunits, among other proteins and RNAs, with leptomycin B also had no obvious effect on nuclear size. Nuclear expansion must now be factored into conceptual and mathematical models of budding yeast growth and division. These results raise questions as to the unknown force(s) that expand the nucleus as yeast cells grow.

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