Answer: The number of molecules inside the cell are [tex]2.2\times 10^6[/tex]
Explanation:
We are given a prokaryotic cell, which is in the shape of rod or cylinder.
The equation used to calculate the volume of cylinder is:
[tex]V=\pi r^2h[/tex]
where,
V = volume of cell = ?
r = radius of the celle = [tex]\frac{d}{2}=\frac{1.7\mu m}{2}=0.85\mu m=8.5\times 10^{-7}m[/tex] (Conversion factor: [tex]1m=10^6\mu m[/tex] )
h = length of the cell = [tex]3.1\mu m=3.1\times 10^{-6}m[/tex]
Putting values in above equation, we get:
[tex]V=(3.14)\times (8.5\times 10^{-7})^2\times 3.1\times 10^{-6}\\\\V=7.033\times 10^{-18}m^3[/tex]
To calculate the number of moles for given molarity of solution, we use the equation:
[tex]\text{Molarity of the solution}=\frac{\text{Moles of solute}}{\text{Volume of solution (in L)}}[/tex]
Molarity of biomolecule = 0.0051 M
Volume of solution = [tex]7.033\times 10^{-18}m^3=7.033\times 10^{-15}L[/tex] (Conversion factor: [tex]1m^3=1000L[/tex] )
Putting values in above equation, we get:
[tex]0.0051M=\frac{\text{Moles of biomoleculel}}{7.033\times 10^{-15}L}\\\\\text{Moles of biomolecule}=(0.0051mol/L\times 7.033\times 10^{-15}L)=3.59\times 10^{-17}mol[/tex]
According to mole concept:
1 mole of a compound contains [tex]6.022\times 10^{23}[/tex] number of molecules
So, [tex]3.59\times 10^{-17}[/tex] moles of a biomolecule will contain = [tex](3.59\times 10^{-17}\times 6.022\times 10^{23}=2.2\times 10^6[/tex] number of molecules
Hence, the number of molecules inside the cell are [tex]2.2\times 10^6[/tex]