Cell Theory & Microscopy

Q1. (3 marks) — 1 mark 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).

Why: These are the three classical tenets synthesising the work of Schleiden, Schwann and Virchow.

Q2. (5 marks) — 1 mark each:

• (a) Hooke — first observed and named "cells" (in cork, 1665).
• (b) Leeuwenhoek — first observed living microorganisms/"animalcules" (bacteria, protists).
• (c) Schleiden — proposed all plants are made of cells.
• (d) Schwann — proposed all animals are made of cells (co-founded cell theory).
• (e) Virchow — stated omnis cellula e cellula — all cells arise from pre-existing cells.

Q3. (4 marks)

• Magnification (1): the number of times larger an image appears compared with the actual (real) size of the object. Ratio image size : actual size (1).
• Resolution (1): the minimum distance between two points at which they can still be distinguished as separate (ability to reveal detail) (1).
• Difference (1): magnification only enlarges; increasing it beyond the resolving limit gives a bigger but blurred image ("empty magnification"). Resolution sets the true detail limit.

Q4. (4 marks) — 1 each:

• (a) $2.5\ \text{mm} \times 1000 = 2500\ \mu\text{m}$
• (b) $750\ \text{nm} \div 1000 = 0.75\ \mu\text{m}$
• (c) $0.02\ \text{mm} \times 10^6 = 20000\ \text{nm}$
• (d) $8000\ \text{nm} \div 10^6 = 0.008\ \text{mm}$

Why: $1\ \text{mm}=1000\ \mu\text{m}=10^6\ \text{nm}$; $1\ \mu\text{m}=1000\ \text{nm}$.

Q5. (3 marks)

• Convert to same units: image $50\ \text{mm} = 50000\ \mu\text{m}$ (1).
• $\text{Mag} = \dfrac{\text{image size}}{\text{actual size}} = \dfrac{50000}{20}$ (1).
• $= \times 2500$ (1).

Q6. (5 marks) (a) Scale bar: image $40\ \text{mm}=40000\ \mu\text{m}$ represents $10\ \mu\text{m}$.

• $\text{Mag} = 40000/10 = \times 4000$ (2).

(b) Actual size $=\dfrac{\text{image size}}{\text{mag}} = \dfrac{25\ \text{mm}}{4000} = \dfrac{25000\ \mu\text{m}}{4000}$ (2).

• $= 6.25\ \mu\text{m}$ (1).

Q7. (5 marks) — table 1 mark per correct row-pair completion (4) + SEM difference (1):

• SEM difference: SEM scans the surface giving a 3-D image; TEM passes electrons through a thin section giving a 2-D internal image (1).

Q8. (4 marks)

• Purpose (2): stains add contrast/colour to otherwise transparent cells, making cells and specific structures visible/distinguishable.
• Examples (1 each, any two): iodine — stains starch blue-black; methylene blue — stains nuclei/cheek cells; eosin — stains cytoplasm pink; crystal violet/Gram stain — differentiates bacteria.

Q9. (4 marks) — 1 mark per correct step / ordering:

1. Place a drop of water (or stain) on a clean glass slide.
2. Place the thin specimen in the drop using forceps/mounted needle.
3. Add a stain if required.
4. Lower a coverslip at an angle (using a needle) to avoid trapping air bubbles. (Blot excess liquid — acceptable extra step.)

Q10. (3 marks)

• $0.1\ \text{mm} = 0.1 \times 10^6\ \text{nm} = 100000\ \text{nm}$ (equivalently $100\ \mu\text{m}$) (2).
• Bacterium $2\ \mu\text{m} < 100\ \mu\text{m}$ resolving limit ⇒ cannot be seen with the naked eye (1).

[
  {"claim":"Q5 magnification = 2500", "code":"image=Rational(50*1000); actual=20; mag=image/actual; result=(mag==2500)"},
  {"claim":"Q6a magnification = 4000", "code":"bar_img=40*1000; bar_real=10; mag=bar_img/bar_real; result=(mag==4000)"},
  {"claim":"Q6b actual size = 6.25 um", "code":"img=25*1000; mag=4000; actual=Rational(img,mag); result=(actual==Rational(25,4))"},
  {"claim":"Q4 conversions correct", "code":"a=2.5*1000; b=750/1000; c=0.02*10**6; d=8000/10**6; result=(a==2500 and abs(b-0.75)<1e-9 and c==20000 and abs(d-0.008)<1e-9)"},
  {"claim":"Q10 0.1 mm = 100000 nm", "code":"nm=0.1*10**6; result=(nm==100000)"}
]