The Nucleus

Rutherford's gold foil experiment first introduced the idea of a nucleus within the atom. The nucleus is several orders of magnitude smaller than the atom. Nearly all the mass and all of the positive charge resides in the nucleus.

How large is the nucleus?

The radius of a nucleus can be approximated by using the following formula.

                                r = (1.2 x 10 ^-15 m) x (#p + #n)^1/3

The volume of the nucleus can be determined by using the formula for the volume of a sphere.

                                        V = 4/3 x p x r³

The nucleus contains:

Surrounding the nucleus is the electron cloud

In all atoms except for hydrogen, there is more than 1 proton in the nucleus. Since like charges repel, one would expect the nucleus to be highly unstable and would disintegrate immediately due to this repulsive electrostatic force. In fact nuclei are stable due to the presence of the strong nuclear force. The strong force is much stronger than the electrostatic repulsive force, but acts over a very small distance (<10^-15 m). The strong force diminishes rapidly as the distance increases.

Radioactive Decay

Radioactive Decay - the release of particles or energy from an unstable nucleus.

Types of Radioactive Decay

1)     Alpha Decay (a) - Helium Nucleus

2)     Positive or negative Beta decay (b) - positron or electron

3)     Gamma decay (g) - high energy photon emitted when a nucleus in a higher energy state "returns" to a lower energy state

4)     Electron Capture - an electron is captured by the nucleus

Transmutations involving alpha and beta particles.

1)     Alpha particle decay results in a product with an atomic mass smaller by 4 amu's and an atomic number smaller by 2.

2)     Positive beta decay and electron capture result in a product with the same atomic mass but an atomic number smaller by 1.

3)     Negative beta decay results in a product with the same atomic mass but an atomic number larger by 1.

Decay Series

Many times a radioactive element decays into another radioactive element. Eventually after a series of decays, a stable non-radioactive element is the final product.

Rate of Decay - Half life

Half life - the amount of time it takes for a radioactive nuclide to decay to half of the original amount

                        N = N_oe^-kt                                                            R = R_oe^-kt

                        ln (N/N_o) = - lt                                                       ln (R/R_o) = - kt
 

                        N = amount of nuclide left                                    R = rate of decay
                        N_o = original amount of nuclide                          R_o = original rate of decay
                        k= decay constant
                        t = time
 

                        t_1/2 = 0.693/l                            k= 0.693 / t_1/2

Radioactive Dating

The source of all carbon in living organisms is CO₂ in the atmosphere. There is some C - 14 in atmospheric CO₂ due to the collision of free neutrons from cosmic rays with atmospheric nitrogen

                                                                    N-14 + n --> C-14 + p

The half life of C-14 is about 5,730 years. Radiocarbon dating is good for carbon based artifacts up to 40, 000 - 60,000 years old. Other radioactive nuclides such as potassium and uranium can be used for dating older materials.

Nuclear Energy

Fission - the splitting of nuclei with atomic number of 92 or greater. The result is 2 smaller nuclei and energy released.

                                                 U - 235 + n ---> U - 236 --> 2 smaller nuclei + Energy

Fusion - 2 smaller nuclei come together to form a larger nucleus. This is how stars produce heat and light. It is also the explanation of how the larger elements were formed.

                                                            2 Hydrogens --> Helium + Energy

Applications:

Nuclear power
Chemotherapy
Food irradiation
Radioactive Tracers

Measurement of Radiation