The movement of a molecule across a typical plant cell (about `50mum`) takes approximately 2.5s. At this rate calculate how many years it would take for the movement of molecules over a distance of 1 m within a plant by diffusion alone?

Answer

To solve the problem of how long it would take for a molecule to diffuse over a distance of 1 meter within a plant, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data**:
- The distance a molecule travels across a typical plant cell is 50 micrometers (µm).
- The time taken to travel this distance is 2.5 seconds.

2. **Convert the Distance to Meters**:
- We need to calculate the time for a distance of 1 meter.
- 1 meter = 1,000,000 micrometers (since 1 m = 10^6 µm).

3. **Calculate the Number of 50 µm Segments in 1 m**:
- To find out how many times the molecule needs to travel 50 µm to cover 1 m, we divide the total distance by the distance of one segment:
\[ \text{Number of segments} = \frac{1,000,000 \, \text{µm}}{50 \, \text{µm}} = 20,000 \]

4. **Calculate the Total Time for 1 m**:
- Since it takes 2.5 seconds to travel 50 µm, we multiply the number of segments by the time taken for each segment:
\[ \text{Total time} = 20,000 \times 2.5 \, \text{seconds} = 50,000 \, \text{seconds} \]

5. **Convert Seconds to Years**:
- To convert seconds into years, we need to know how many seconds are in a year. There are approximately 31,536,000 seconds in a year (365 days).
\[ \text{Time in years} = \frac{50,000 \, \text{seconds}}{31,536,000 \, \text{seconds/year}} \approx 0.00159 \, \text{years} \]

6. **Final Calculation**:
- To express this in a more understandable format, we can convert years into days:
\[ \text{Time in days} = 0.00159 \times 365 \approx 0.58 \, \text{days} \]
- Therefore, it would take approximately 0.58 days for a molecule to diffuse 1 meter in a plant.

### Final Answer:
It would take approximately **0.58 days** for the movement of a molecule over a distance of 1 meter within a plant by diffusion alone.