further chem
classical mechanics:

  • energy is continuous, it can take any value
  • we know the position of everything at any time
    • specified
  • can describe aspects of nature at macroscopic and microscopic (visual) scale, but not at atomic and subatomic scales

quantum mechanics:

  • energy is discrete, like a ladder, quantised (bound states)
    • applies to energy, momentum, angular momentum, other quantities
  • more so about the probability of finding an electron at some position
  • can be used to derive classical mechanics as an approximation that is valid at ordinary scales
  • measurements show characteristics of particles and waves, but there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement

Pauli exclusion principle:

  • there cannot be two identical fermions simultaneously having the same quantum numbers

note

\begin{align}
\text{hydrogen atom: }&E(3s)=E(3p)=E(3d) \
\text{multi-electron atoms: }&E(3s)<E(3p)<E(3d)
\end{align}

öö

\underset{\begin{array}{}
\text{effective nuclear charge}
\end{array}}{ Z_\text{eff} }<\underset{\text{actual nuclear charge}}{ Z }

\begin{equation}
Z_\text{eff}=Z-\underset{\begin{array}{}
\text{shielding} \
\text{constant}
\end{array}}{ \sigma }
\end{equation}