Solution for Question (a): Geiger-Marsden Experiment
Step 1 (Graph Representation): [0.5 Mark]
The graph plots the number of scattered alpha particles ($N$) on the y-axis against the scattering angle ($\theta$) on the x-axis. The curve shows an exponential-like decay where $N \propto \frac{1}{\sin^4(\theta/2)}$.
[Graph: A downward sloping curve starting from high $N$ at low $\theta$ and approaching near zero as $\theta$ increases towards 180°]
Step 2 (Inference of Conclusions): [0.5 Mark]
- Conclusion 1: Most of the alpha particles pass through the gold foil with very little or no deflection, indicating that the atom is mostly empty space.
- Conclusion 2: A very small fraction of alpha particles undergo large-angle scattering (or even backscattering), which proves the existence of a small, dense, positively charged central core called the nucleus.
💡 EL10 Concept Insight: Imagine throwing tennis balls at a thin curtain; most go straight through (empty space), but if one hits a hidden bowling ball, it bounces straight back—that "bowling ball" is the nucleus!
Solution for Question (b): Photoelectric Effect Graphs
Step 1 (Governing Law): [0.5 Mark]
The photoelectric current depends on the intensity of incident light, while the stopping potential ($V_0$) depends on the frequency of incident light according to Einstein’s Photoelectric Equation: $K_{max} = h\nu - \Phi_0 = eV_0$.
Step 2 (Step-by-Step Graphical Analysis): [0.5 Mark]
- (i) Same Intensity, Different Frequencies ($\nu_1 < \nu_2 < \nu_3$): The saturation current remains the same for all three, but the stopping potential becomes more negative as frequency increases. $$|V_{0_1}| < |V_{0_2}| < |V_{0_3}|$$
- (ii) Same Frequency, Different Intensities ($I_1 < I_2 < I_3$): The stopping potential remains the same for all three, but the saturation current increases proportionally with intensity. $$I_{sat_1} < I_{sat_2} < I_{sat_3}$$
💡 EL10 Concept Insight: Think of intensity as the "number of bullets" (more current) and frequency as the "speed of the bullets" (more energy to stop them). More bullets mean more hits, but faster bullets need a stronger wall to stop them!