# Atomic Structure

An atom consists of a tighly bounded nucleus sourrounded by a cloud of electrons. This solar-system model was discovered by Rutherford whom was studying the scattering of alpha particles and was an improvement from the soup model suggested by Thompson where protons and electrons, in equal quantities, were uniformly distributed. The solar-system model was further refined by Bohr specifying that electrons exist in discrete energy orbits (later refined as electron clouds where the cloud represents the probability density of the electron). The strong nuclear foce keeps the positively charged nucleus together.

The nucleus is made up of protons and neutrons. The total number of protons is known as the atomic number, $$Z$$, and determines the identity of the atom. The charge of the nucleus is $$+Ze$$ since each proton has a charge $$e$$ and there are $$Z$$ of them. Electrons also contribute to the charge of an atom. In a neutron atom, there are an equal number of electrons and protons and the atom has no charge (i.e., $$-Ze$$).

The number of neutrons is $$N$$, the neutron number. The atomic mass, or nucleon number, is the sum of the number of protons, the atomic number, and the number of neutrons, the neutron number, and is given by $$A = Z + N$$. Recall that protons and nuetrons have roughly the same mass whereas electrons are much ligher.

Various atoms with different numbers of protons and nuetrons are nuclides. A nuclide is denoted by the chemical symbol (such as H, C, Sm, etc.) with the atomic mass, $$A$$ as a superscript such as $$\ce{^4He}$$. For further clarity, the atomic number, $$Z$$ , is sometimes written as a subscript such as $$\ce{^4_2He}$$.

Remember, the atomic number,$$Z$$, is unique to a certain atom. However, the number of neutrons may differ. Atoms with the same atomic number but different atom mass are called isotopes (for example, $$\ce{^16_8O}$$ and $$\ce{^18_8O}$$ ). Atoms with the same atomic number,$$Z$$, and atomic mass, $$A$$, but different mass/energy are isomers (i.e., in an excited state). Unstable isotopes are radioactive and decay into stable atoms using differnt decaying methods. Isotopes occur naturally in different abundancies given in atomic percentage (or a/o).

A Glass of water contains $$4.0\cdot10^{20}$$ atoms of hydrogen. How many atoms of deuterium ($$\ce{^2_1H}$$) are present if the natural abundancy is 0.015 a/o?

## Atomic and Molecular Weight

The atomic weight of an atom is defined as the mass relative to $$\ce{^12C}$$ which is taken arbitrarily as 12. Formally,

$$M(\ce{^AZ}) = 12 \cdot \frac{m(\ce{^AZ})}{m(\ce{^12C})}$$

Isotopes that are naturally occuring have an atomic weight equal to the weighted average of the mixture of all isotopes:

$$M =\frac{\gamma_i}{100} \sum M_i$$

Given the data in the table below, calculate the atomic weight of naturally occuring oxygen.

Isotope Abundance Atomic Weight
$$\ce{^16O}$$ 99.759 15.99492
$$\ce{^17O}$$ 0.037 16.99913
$$\ce{^18O}$$ 0.204 17.99916

How many grams is 3 mols of Cs-133?