Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?

1. Break Down the Problem

To determine how many atoms thick a cell membrane is, we need to know:

• The average thickness of a cell membrane.
• The size of a hydrogen atom to estimate how many atoms fit into that thickness.

2. Relevant Concepts

• Average Thickness of a Cell Membrane: Typically, a cell membrane is about 7.5 nm (nanometers) thick.
• Size of a Hydrogen Atom: The atomic radius of a hydrogen atom is approximately 0.53 Å (angstroms), which is equivalent to $0.53 \, \text{Å} = 0.053 \, \text{nm}$.
• Since the problem states that the average atom size is about twice that of a hydrogen atom, we will calculate using $2 \times 0.53 \, \text{Å} = 1.06 \, \text{Å} = 0.106 \, \text{nm}$.

3. Analysis and Detail

1. Convert the average thickness of the membrane to nanometers: $\text{Thickness of membrane} = 7.5 \, \text{nm}$
2. Calculate the size of the average atom in the membrane: $\text{Size of an atom} = 0.106 \, \text{nm}$
3. Determine how many atoms fit into the thickness of the membrane: $\text{Number of atoms} = \frac{\text{Thickness of membrane}}{\text{Size of an atom}} = \frac{7.5 \, \text{nm}}{0.106 \, \text{nm}} \approx 70.75$

4. Verify and Summarize

Rounding $70.75$ to the nearest whole number gives us approximately 71 atoms. This indicates that the cell membrane is around 71 atoms thick.

Final Answer

The cell membrane is approximately 71 atoms thick.