Biology 9700/11 — October/November 2011

Background Concept

Prokaryotic cells (bacteria and archaea) are much smaller than eukaryotic cells. A typical bacterium such as Streptococcus has a diameter of roughly 0.5–2 µm. By comparison, a typical eukaryotic animal cell is about 10–100 µm across, and a typical plant cell about 10–200 µm. The small size of prokaryotes is one reason they have a very high surface area to volume ratio, which is important for the rapid exchange of materials across the plasma membrane by diffusion.

Unit conversions in microscopy:

• $1\ \text{µm} = 10^3\ \text{nm} = 1000\ \text{nm}$
• $1\ \text{nm} = 10^{-3}\ \text{µm} = 0.001\ \text{µm}$

Understanding the Question

This is a multiple-choice question (Paper 1) that tests two things at once: (1) knowledge of the typical size of a prokaryotic cell, and (2) the ability to convert between nanometres and micrometres. The four options are all expressed in different orders of magnitude or units, so a quick unit conversion exposes the correct answer.

Approach

Convert each option into a single, common unit (µm is convenient) and compare the resulting number to the known size range of a typical bacterium (~0.5–2 µm diameter). The option that falls within this range is the answer.

Step-by-Step Reasoning

• Option A: $7.5 \times 10^1\ \text{nm} = 75\ \text{nm}$. Convert: $75 \div 1000 = 0.075\ \text{µm}$. This is far too small — only large viruses approach this size.
• Option B: $7.5 \times 10^2\ \text{nm} = 750\ \text{nm}$. Convert: $750 \div 1000 = 0.75\ \text{µm}$. This lies comfortably within the 0.5–2 µm range for typical bacteria, including Streptococcus.
• Option C: $7.5 \times 10^0\ \text{µm} = 7.5\ \text{µm}$. This is too large for a prokaryote; it is more in the size range of small eukaryotic cells or organelles such as the nucleus.
• Option D: $7.5 \times 10^1\ \text{µm} = 75\ \text{µm}$. This is comparable to a typical eukaryotic animal cell and far too large for a bacterium.

Therefore, option B is the only value consistent with a typical prokaryotic diameter.

Key Takeaways

• Typical prokaryotic cell diameter: ~0.5–2 µm (or 500–2000 nm).
• $1\ \text{µm} = 10^3\ \text{nm}$, so always convert to a common unit before comparing values.
• Prokaryotes are roughly 10–100× smaller than eukaryotic cells.

Common Mistakes

• Not converting units before comparing — a number in nm looks larger than the equivalent value in µm and can mislead.
• Confusing prokaryote size with virus size (~20–300 nm) or eukaryotic cell size (~10–100 µm), leading to the wrong order of magnitude.

Things to Be Careful About

• Standard form in the options ($7.5 \times 10^1$, $7.5 \times 10^2$, etc.) must be evaluated correctly — $7.5 \times 10^0 = 7.5$, not 0.
• The answer is the option whose converted value sits in the typical prokaryotic range, not just the option that looks smallest.