Question

At the normal rate, calculate how many years it would take for the movement of molecules over a distance of 1 m within a plant by diffusion process alone.
a. Approximately 1 year
b. Approximately 2 years
c. Approximately 3 months
d. Cannot be Approximated

Answer 1

Hint: As we know that molecules travel approximately 50 picometer in 2.5 seconds, when it moves only by diffusion, which is a process that involves independent movement of molecules, based on their concentration gradient and size.

Complete answer:
Molecules move from higher concentration of solutes to their lower concentrations through diffusion. Many microorganisms use this method to take-up food molecules inside the cell. This movement of molecules also depends upon size of molecules. The small molecules will easily pass by semipermeable membrane but large molecules will not be able to cross the membrane because of large size compared to size of membrane.

Similarly, the plants also use this method for transferring various food molecules from leaves to other parts of the body or for water molecules or minerals, from roots to the other parts of the plant.

Let us assume that only diffusion is happening inside the plant, and then we know that molecules will move with a speed of 50 picometer in 2.5 seconds.

Now, we also know that $1m=1\times {{10}^{-12}}\text{picometer}$.
Thus, to travel 1m, we can calculate the time using,
$\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}$
$\text{Time}=\dfrac{1\times 10^{-12} \times 2.5}{5}=5\times {{10}^{-11}}s$
We know that the total number of seconds in a year is $3.2\times {{10}^{7}}s$.

Thus, we can calculate the number of years using,
$\text{Number Of Years}=\dfrac{\text{Total seconds calculated}}{\text{Total second in a year}}$
$=\dfrac{5\times {{10}^{-11}}}{3.2\times {{10}^{7}}}=1.5\times {{10}^{3}}years$
The number of years, $1.5\times {{10}^{3}}$, is approximately equal to 2 years. Hence, we can say that it will take the molecules approximately 2 years to travel a distance of 1m by diffusion only.

Hence, the correct answer is option (B).

Note: Diffusion is when a simple molecule moves through a semipermeable membrane or in a solution without any help from transport protein and facilitates diffusion, which is passive movement of molecules from higher to lower concentration region by means of a carrier molecule. The factors influencing diffusion are temperature, pressure, density and concentration. Diffusion is directly proportional to concentration and temperature.