Cell Theory & Microscopy

Question 1

(a) (3 marks, 1 each)

1. All living organisms are composed of one or more cells.
2. The cell is the basic (structural and functional) unit of life.
3. All cells arise from pre-existing cells (by division).

(b) (5 marks, 1 each)

• Hooke (1665): first observed and named "cells" in cork — established the term/observational foundation.
• Leeuwenhoek (~1674): first observed living single-celled organisms ("animalcules") with improved single-lens microscopes — extended Hooke's dead-cork observation to living cells, proving cells were not just empty boxes.
• Schleiden (1838): concluded all plants are made of cells — generalised isolated observations into a plant-wide principle.
• Schwann (1839): extended Schleiden's plant conclusion to animals, unifying both into tenets 1 & 2.
• Virchow (1855): added tenet 3 (cells from pre-existing cells) — completed Schleiden/Schwann's theory by explaining cell origin.

Marking: full mark requires contribution and the logical dependency/extension.

(c) (4 marks)

• Contradicted hypothesis: spontaneous generation (abiogenesis). (1)
• Argument: Observation alone shows cells exist, not their origin. (1) A snapshot cannot distinguish "cell arose from a parent cell" from "cell arose spontaneously from non-living matter." (1) Only a controlled experiment (e.g. sterilised vs exposed broth, isolating the variable of prior cell presence — as later done by Pasteur) can establish causation of origin. (1)

(d) (6 marks)

• Magnification = ratio of image size to actual size (how much larger it appears); no units. (1)
• Resolution = minimum distance $d$ at which two points are seen as separate; a physical limit. (1)
• Diffraction limit $d = \dfrac{\lambda}{2\,\text{NA}}$: $\lambda$ = wavelength of illuminating radiation, NA = numerical aperture of the lens system. (2 — formula + symbol definitions)
• Proof of empty magnification: $d$ depends only on $\lambda$ and NA, not on magnification. (1) Once you magnify beyond the point where features smaller than $d$ would need to be separated, no new detail appears — the image just becomes bigger and blurrier. Hence magnification $>$ resolving power = "empty magnification." (1)

Question 2

(a) (4 marks) Magnification = image size of scale bar ÷ actual size it represents. $M = \frac{40\ \text{mm}}{2\ \mu\text{m}} = \frac{40\,000\ \mu\text{m}}{2\ \mu\text{m}} = 20\,000\times$ (unit conversion 1; ratio 2; final ×20 000 = 1)

(b) (5 marks) Actual length = image length ÷ magnification: $L = \frac{100\ \text{mm}}{20\,000} = 0.005\ \text{mm} = 5\ \mu\text{m}$ (2) Convert:

• $5\ \mu\text{m} = 5000\ \text{nm}$ (1)
• $5\ \mu\text{m} = 0.005\ \text{mm}$ (1)
• Method (÷ M) correct (1)

(c) (6 marks)

• TEM: $d = \dfrac{0.005}{2\times0.02} = \dfrac{0.005}{0.04} = 0.125\ \text{nm}$ (2)
• Light: $d = \dfrac{500}{2\times1.25} = \dfrac{500}{2.5} = 200\ \text{nm}$ (2)
• Ratio (improvement) = $200 / 0.125 = 1600$ — TEM resolves ~1600× finer detail. (2)

(d) (3 marks)

• Light microscope: $d = 200\ \text{nm} > 30\ \text{nm}$ separation → cannot resolve the two ribosomes. (1.5)
• TEM: $d = 0.125\ \text{nm} \ll 30\ \text{nm}$ → can easily resolve them. (1.5)

(e) (6 marks)

def actual_size(bar_label_um, bar_px, object_px):
    um_per_px = bar_label_um / bar_px      # calibration
    return object_px * um_per_px

(function logic 4) For bar_label = 2, bar_px = 40, object_px = 100: $\text{um\_per\_px} = 2/40 = 0.05;\quad 100 \times 0.05 = 5.0\ \mu\text{m}$ Output = 5.0 µm, matching part (b). (2)

Question 3

(a) (6 marks — 1 step + purpose each, 3 pairs)

1. Place a drop of water on a clean slide — provides medium, keeps cells hydrated/prevents shrivelling.
2. Peel/place a thin specimen (single cell layer) into the drop — thin sample lets light pass for viewing.
3. Lower a coverslip at ~45° using a mounted needle — avoids trapping air bubbles which obscure the image.
4. (Add stain at coverslip edge; draw through with paper if staining) — increases contrast.

(b) (4 marks)

• Cells are mostly transparent → low contrast. Stains bind selectively (differential absorption) so certain structures (e.g. nuclei) absorb light/appear coloured, standing out. (2)
• Disadvantage: most stains are toxic/kill cells, so they cannot be used to observe living processes (dynamics, movement) in real time. (2)

(c) (4 marks — table, ~0.5 per correct cell + coherence)

(d) (4 marks)

• Higher magnification is useless beyond the resolution limit → "empty magnification." (2)
• Also, best microscope depends on purpose: e.g. light microscopes allow viewing living specimens in colour, which EM cannot. So "always better" is false; choice is task-dependent. (2)

[
  {"claim":"Micrograph magnification = 40mm/2um = 20000x","code":"bar_mm=40; bar_um=bar_mm*1000; actual_um=2; M=bar_um/actual_um; result=(M==20000)"},
  {"claim":"Chloroplast actual length = 5 um (=5000nm =0.005mm)","code":"img_mm=100; M=20000; L_mm=img_mm/M; L_um=L_mm*1000; L_nm=L_um*1000; result=(L_um==5 and L_nm==5000 and L_mm==Rational(5,1000))"},
  {"claim":"TEM resolution=0.125nm, Light=200nm, ratio=1600","code":"d_tem=Rational(5,1000)/(2*Rational(2,100)); d_light=Rational(500)/(2*Rational(125,100)); ratio=d_light/d_tem; result=(d_tem==Rational(1,8) and d_light==200 and ratio==1600)"},
  {"claim":"actual_size(2,40,100) returns 5.0 um","code":"def actual_size(b,bp,op): return op*(b/bp)\nresult=(actual_size(2,40,100)==5)"}
]