Data Transformation, Filtering & Physical Slicing
Mathematical Problem Formulation
Physical Law: Einstein's Photoelectric Equation:
When monochromatic light of frequency $\nu = \frac{c}{\lambda}$ strikes a photocathode, the maximum kinetic energy $K_{\text{max}}$ of emitted photoelectrons is given by Einstein's relation:
$$K_{\text{max}} = e V_0 = h \nu - \Phi$$
where $V_0$ is the stopping potential (in Volts), $e$ is the elementary charge ($1.602 \times 10^{-19}\,\text{C}$), $h$ is Planck's constant, and $\Phi$ is the work function of the material.
Condition for Active Photoelectric Emission:
Photoemission occurs exclusively when photon energy exceeds the work function:
$$h \nu > \Phi \iff V_0 > 0$$
The slope of stopping potential versus optical frequency yields Planck's constant:
$$\frac{dV_0}{d\nu} = \frac{h}{e} \implies h = e \left( \frac{\Delta V_0}{\Delta \nu} \right)$$
Theoretical Background & Explanation
1. Filtering & Relational Slicing in Experimental Physics:
Physical experiments often encompass multiple regimes (e.g., sub-threshold non-emission vs above-threshold photoemission). Pandas enables instantaneous filtering using boolean conditions (such as df[df['stopping_potential_V'] > 0]) without mutating original records.
2. Multi-Dataset Merging & Concatenation:
In experimental laboratories, measurements on different materials (e.g., Cesium vs Potassium cathodes) are often logged in separate trials. pd.concat() unifies them into a comprehensive comparative ledger, while .sort_values() organizes them monotonically by frequency.
3. Derivation of Fundamental Physical Constants:
By extracting active rows from the filtered DataFrame and computing differential ratios $\frac{\Delta V_0}{\Delta \nu}$, students determine experimental values of Planck's constant $h$ directly from laboratory data.