The scale of cells and organelles
- Cells and organelles are far too small to measure comfortably in millimetres, so biologists work in micrometres and nanometres.
- A typical animal cell is around 20 μm20\,\mu\text{m}20μm across, and a plant cell is usually larger at 505050 to 100 μm100\,\mu\text{m}100μm.
- A bacterial cell is about 2 μm2\,\mu\text{m}2μm long, roughly ten times smaller than an animal cell.
- Inside a cell, a nucleus is around 6 μm6\,\mu\text{m}6μm across and a mitochondrion about 2 μm2\,\mu\text{m}2μm long.
- A ribosome is only about 20 nm20\,\text{nm}20nm across, a thousand times smaller again, which is why a light microscope cannot resolve one.
- Being able to put these in order matters more than memorising exact values, because Edexcel asks you to compare scales rather than recite figures.
Note
Each factor of ten is one order of magnitude, so a 20 μm20\,\mu\text{m}20μm animal cell is about one order of magnitude larger than a 2 μm2\,\mu\text{m}2μm bacterium and three orders of magnitude larger than a 20 nm20\,\text{nm}20nm ribosome.
The magnification equation
Definition
Magnification
The number of times larger an image is than the actual object it shows.
- Magnification links the size of an image to the real size of the object it shows.
- magnification=image sizeactual size\text{magnification} = \dfrac{\text{image size}}{\text{actual size}}magnification=actual sizeimage size
- Rearranging it gives the form you need whenever a question supplies the magnification and asks for the real size.
- actual size=image sizemagnification\text{actual size} = \dfrac{\text{image size}}{\text{magnification}}actual size=magnificationimage size
- Magnification has no units, because it is one length divided by another, and it is written with a multiplication sign such as ×400\times 400×400.
- Both lengths have to be in the same unit before you divide.
- On a light microscope the total magnification is the eyepiece lens multiplied by the objective lens in use.
Common Mistake
Almost every lost mark on these questions comes from dividing a length in millimetres by a length in micrometres, so convert the units first and write the conversion down.
Example
- A drawing of a cheek cell measures 60 mm60\,\text{mm}60mm across and is labelled ×1000\times 1000×1000.
- Convert the image size into micrometres, since the answer will be a cell size: 60 mm=60×1000=60 000 μm60\,\text{mm} = 60 \times 1000 = 60\,000\,\mu\text{m}60mm=60×1000=60000μm.
- Now divide the image size by the magnification.
- actual size=60 0001000=60 μm\text{actual size} = \dfrac{60\,000}{1000} = 60\,\mu\text{m}actual size=100060000=60μm
- Check the answer against what you know, because 60 μm60\,\mu\text{m}60μm is a sensible size for a cheek cell.
Hint
An answer in the millions or in tiny fractions is usually a sign that a unit conversion has been missed.
Example
- An electron micrograph shows a mitochondrion measuring 40 mm40\,\text{mm}40mm long, and its actual length is 2 μm2\,\mu\text{m}2μm.
- Convert the image size into the same unit as the actual size: 40 mm=40 000 μm40\,\text{mm} = 40\,000\,\mu\text{m}40mm=40000μm.
- Divide the image size by the actual size.
- magnification=40 0002=20 000\text{magnification} = \dfrac{40\,000}{2} = 20\,000magnification=240000=20000
- Write the answer as ×20 000\times 20\,000×20000 and give it no units.
Exam technique
- Set the working out in three lines, equation, substitution, answer, because a conversion error still earns method marks if the examiner can see the equation.
- Measure the image yourself with a ruler when the question tells you to, and give the measurement in millimetres before converting.
- Read the unit demanded in the answer line, since a question that asks for micrometres will not credit an answer left in millimetres.
When to use an estimate
Definition
Estimate
An approximate value worked out from rounded figures, used when an exact measurement is not needed or not possible.
- Use an estimate when an exact measurement is not possible, such as when cells overlap or run off the edge of the field of view.
- Use one when the quantity naturally varies, because cells in the same tissue are not all the same size and a single exact value would be misleading.
- Use one to check a calculated answer, since an estimate quickly shows whether a result is the right order of magnitude.
- To estimate a cell size, lay a transparent ruler across the field of view and measure its diameter, then count how many cells span it.
- If the field of view is 4.5 mm4.5\,\text{mm}4.5mm across and 151515 onion cells fit end to end along it, convert to 4500 μm4500\,\mu\text{m}4500μm and divide.
- estimated cell length=450015=300 μm\text{estimated cell length} = \dfrac{4500}{15} = 300\,\mu\text{m}estimated cell length=154500=300μm
- Say clearly that the value is an estimate and give one reason, for example that the cells are not all identical in length.
Self review
- Write the magnification equation and both of its rearranged forms.
- Why does magnification have no units?
- An image is 30 mm30\,\text{mm}30mm wide at ×500\times 500×500, so what is the actual width in micrometres?
- Put a bacterium, a ribosome and a plant cell in order of size, smallest first.
- Give two situations in which an estimate is more appropriate than an exact measurement.
