ARCH-B-12: Photosynthesis Inverse-Square Law (I ∝ 1/d^2), Limiting Factors & Capillary Potometers (πr^2h/t)

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-B-12: Why the 145s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~145s (Blows 90s Clock)

By the inverse-square law, light intensity

I

is inversely proportional to the square of the distance

d

from a point source:

\frac{R_2}{R_1} = \frac{I_2}{I_1} = \left(\frac{d_1}{d_2}\right)^2 = \left(\frac{20}{40}\right)^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}

R_2 = \frac{64}{4} = \mathbf{16\text{ bubbles min}^{-1}}

The Fast ShortcutTarget: 40s (Saves 105s)

Distance doubles (

20 \to 40\text{ cm}

)

\implies I

drops by

2^2 = 4 \implies R_2 = \frac{64}{4} = \mathbf{16\text{ bubbles min}^{-1}}

Where Students Lose Time: In 21 past UAT-UK questions (9.01% of Biology), candidates lose 105s by classic potometer trap: failing to halve capillary internal diameter d to radius r = d/2 before squaring. Instead, apply B11 with Maths 1 skill M3.4.

Step 1 of 6 • Press ArrowRight or Space