Cells: size, magnification and surface area
Prokaryotic and eukaryotic cells, magnification and resolution, surface-area-to-volume ratio, and estimating the size of onion cells from the field of view.
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Prokaryotic cells (bacteria and archaea) have no nucleus and no membrane-bound organelles; their DNA lies in the nucleoid. They are 0.1–5.0 µm across. Eukaryotic cells, such as plant and animal cells, have a nucleus and are typically 10–100 µm across.[2]
Magnification is how much bigger an object looks; resolution (resolving power) is the ability to see two close structures as separate. Electron microscopes give higher magnification and resolution than light microscopes.[1]
For a light microscope, total magnification = eyepiece magnification × objective magnification: a 10× eyepiece and a 40× objective give 400×. So an 8 µm red blood cell appears 400 × 8 µm = 3.2 mm wide. Rearranged: actual size = image size ÷ magnification.[4][1]
Why are cells small? For a sphere, A = 4πr² and V = 4πr³/3, so A/V = 3/r. Doubling the radius halves the surface area per unit volume, and a cell that is too large may not have enough membrane for diffusion. Cells cope by dividing, being thin or elongated, or folding their membranes.[2]
Organelles divide the work: the nucleus holds the DNA, ribosomes make proteins, mitochondria make ATP by cellular respiration and chloroplasts carry out photosynthesis.[3]
An adult human has about 30 trillion human cells of about 200 types, and roughly as many bacterial cells. About 330 billion cells are replaced each day, mostly blood cells and cells lining the gut. These are estimates, not exact counts.[5]
Try it: How big is an onion cell?
You need
- Onion epidermis (prepared as a wet mount)
- Microscope slides, coverslips, tweezers, dropper
- Dilute iodine solution from the school stain kit
- Light microscope with 10× eyepiece and 4×, 10× and 40× objectives
- Clear plastic ruler with mm markings
- Gloves and eye protection
Safety
Wear eye protection and gloves when using iodine solution; it stains skin and clothing and irritates eyes, so rinse any splashes with water and tell the teacher. Handle slides and coverslips by the edges and report breakages. Never use direct sunlight as the light source.
What to do
- Prepare a wet mount of onion epidermis with one drop of dilute iodine solution; lower the coverslip at an angle to avoid bubbles.
- At the lowest total magnification (10× × 4× = 40×) place the clear ruler on the stage and measure the diameter of the field of view in mm.
- Replace the ruler with your slide. Count how many cells lie end to end across the diameter of the field of view.
- Estimate one cell's length: field-of-view diameter ÷ number of cells. Convert to µm (1 mm = 1000 µm).
- Repeat the count in two other places on the slide, take the mean, and state the uncertainty (half the range of your three results).
What happens, and why?
Total magnification is the eyepiece magnification times the objective magnification, so you know how much you are enlarging. Measuring the field of view with a ruler at low power and counting cells across it gives an estimate of the real cell size. Stains make transparent cells and their nuclei visible but usually kill the cells.[4][1]
Play: Prokaryote or eukaryote?
Does each feature belong to prokaryotic cells, eukaryotic cells, or both?
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Quiz
Other ages: Ages 6–7 · Ages 10–11