Microscopy Practical and Size Estimation

When labelling, use a ruler to draw label lines. These lines must not cross each other, must not have arrowheads, and must touch the specific structure being labelled. For plant cells, the thickness of the cell wall must be represented by two distinct parallel lines, not a single thick line.

AQA strictly requires a magnification scale on your drawings. This is often done using a scale bar, which is a line drawn on a diagram that represents a specific actual length.

Worked Example: Drawing a Scale Bar

• Step 1: Measure the length of your cell drawing in mm (e.g., $50\ \text{mm}$).

• Step 2: Determine the actual size of the cell (e.g., $100\ \mu\text{m}$).

• Step 3: Calculate the drawing's magnification: $50,000\ \mu\text{m} / 100\ \mu\text{m} = \times 500$.

• Step 4: Choose a sensible scale bar length representing about 20% of the drawing (e.g., $20\ \mu\text{m}$). Calculate how long to draw this line:

• Step 5: Draw a $10\ \text{mm}$ line using a ruler and label it "$20\ \mu\text{m}$".

Estimating Cell Size, Area, and Magnification

You can snap a ruler in half easily, but trying to measure a single microscopic cell requires a totally different approach to mathematics. Before calculating sizes, you must be confident with unit conversions.

The standard unit for cells is the micrometre ($\mu\text{m}$):

• $1\ \text{mm} = 1,000\ \mu\text{m}$
• $1\ \mu\text{m} = 1,000\ \text{nm}$ (nanometres)

Total magnification is calculated by multiplying the eyepiece lens magnification by the objective lens magnification. Magnification itself is the number of times larger an image appears compared to the real size of the object.

The standard formula is:

(Image Size = Actual Size \times Magnification)

Worked Example: Estimating Cell Size using FOV

You place a clear ruler on the stage and measure the FOV diameter as $2\ \text{mm}$. You count 40 cells fitting across this diameter. Estimate the length of one cell.

• Step 1: Convert the FOV into $\mu\text{m}$: $2\ \text{mm} \times 1,000 = 2,000\ \mu\text{m}$.

• Step 2: Divide the FOV by the number of cells: $2,000\ \mu\text{m} / 40 = 50\ \mu\text{m}$ per cell.

Worked Example: Estimating Organelle Area

A cell has an area of $5,000\ \mu\text{m}^2$. Approximately 20 nuclei fit inside this cell. Estimate the area of one nucleus.

• Step 1: Divide the total area by the number of structures that fit inside.

• Step 2: $5,000\ \mu\text{m}^2 / 20 = 250\ \mu\text{m}^2$.

Orders of Magnitude and Standard Form

Understanding absolute sizes is useful, but comparing the relative scales of structures helps us understand how they fit together. Standard form is a way of writing very large or small numbers as a number between 1 and 10 multiplied by a power of 10.

An order of magnitude is a power of 10 used to compare the scale of two values. If value A is 10 times larger than value B, it is one order of magnitude larger ($10^1$). If it is 100 times larger, it is two orders of magnitude larger ($10^2$).

You must know the sub-cellular hierarchy from smallest to largest:

• Ribosome: $2 \times 10^{-8}\ \text{m}$ ($20\ \text{nm}$)
• Virus: $1 \times 10^{-7}\ \text{m}$ ($100\ \text{nm}$)
• Bacterium: $1 \times 10^{-6}\ \text{m}$ ($1\ \mu\text{m}$)
• Mitochondrion: $2 \times 10^{-6}\ \text{m}$ ($2\ \mu\text{m}$)
• Nucleus: $1 \times 10^{-5}\ \text{m}$ ($10\ \mu\text{m}$)
• Animal Cell: $2 \times 10^{-5}\ \text{m}$ ($20\ \mu\text{m}$)

Worked Example: Calculating Order of Magnitude Difference

A plant cell is $100\ \mu\text{m}$ ($1 \times 10^{-4}\ \text{m}$) and a bacterium is $1\ \mu\text{m}$ ($1 \times 10^{-6}\ \text{m}$). Calculate the order of magnitude difference.

• Step 1: Divide the larger value by the smaller value: $100 / 1 = 100$.

• Step 2: Convert the result to a power of 10: $100 = 10^2$.

• Step 3: State the final answer: There is a difference of 2 orders of magnitude.