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}
\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}