KHAEMENES ACADEMY · BIOLOGY 10 · WEEK 06 · DAY 04

Diffusion Model Laboratory: Distance, Time & Percent Penetration

Use a safe model or supplied dataset to quantify diffusion distance and evaluate how size changes the fraction of a model reached by diffusion.

Safety and evidence boundary

Preferred route: use the supplied dataset or paper/computational model. A teacher-supervised agar-cube demonstration is optional only if materials, supervision, and disposal procedures are appropriate. Do not improvise indicators, acids, bases, or unknown reagents at home.

Explicit science instruction

Diffusion models often compare differently sized cubes exposed to the same external condition. If a substance penetrates a similar distance from each surface in the same amount of time, a smaller cube can have a larger fraction of its volume reached.

Use this synthetic model: after a fixed interval, penetration depth is 0.5 cm from every surface. For a 1 cm cube, penetration reaches the center, so modeled penetration is 100%. For a 2 cm cube, the unpenetrated inner cube has side 1 cm, volume 1 cm³. Total volume is 8 cm³, so penetrated volume = 7 cm³ and percent penetrated = 7/8 × 100 = 87.5%.

This is a geometry model, not direct evidence about real cells. Living cells contain membranes, active transport, cytoskeletal organization, organelles, and fluid movement that are absent from an agar cube.

Vocabulary: diffusion distance; penetration depth; percent penetrated; model; control; repeated trial; uncertainty; extrapolation.

Worked example with reasoning

For a 3 cm cube with 0.5 cm penetration from every side, the unpenetrated inner side length is 3 − 1 = 2 cm. Inner volume = 2³ = 8 cm³. Total volume = 3³ = 27 cm³. Penetrated volume = 27 − 8 = 19 cm³. Percent penetrated ≈ 19/27 × 100 = 70.4%.

Guided question

Why does the 3 cm cube have a lower percentage penetrated than the 2 cm cube even though the penetration depth is identical?

Independent work

  1. Calculate percent penetrated for 1, 2, 3, and 4 cm cube models using 0.5 cm depth.
  2. Graph cube side length against percent penetrated.
  3. Identify independent, dependent, and controlled variables in the model.
  4. Write two reasons a real cell differs from an agar cube.
  5. Propose one safe follow-up model that changes only one variable.

Misconception check

Diffusion distance is not automatically faster in a smaller cube. The important result here is the fraction of the model reached relative to its size under the same penetration depth and time.

Formative understanding check

Why is an agar-cube model useful but insufficient for claiming an exact maximum cell size?

Show the worked response

It illustrates geometry and diffusion-distance constraints, but real cells have active transport, dynamic membranes, internal transport, metabolism, varied shapes, and many other features not represented by agar.

Open-book formative practice only; not an official mastery attempt or grade.

Mentor evidence conference

Ask the mentor to check your inner-cube geometry and then identify one place where you might accidentally generalize a model result to real cells too strongly.

Open Archaemenes for this lesson

Teacher guidance

Foundation: use supplied 1–3 cm calculations. Core: calculate percent penetrated and graph the pattern. Extended: derive the inner-volume expression (s−2d)³ and discuss assumptions.

Preserve learning evidence

Preserve the calculations, graph, variable table, two model limitations, and follow-up design in Thursday’s evidence field.

Return to thursday Evidence Workspace