Answer : Total molecules that will be needed to visualize a single egg will be 78500 molecules of dye.
Explanation : As a single egg cell has an approximately diameter of 100 μm.
We can use this formula to calculate area of the cell membrane;
A = π [tex] (100)^{2} / 4 [/tex];
We can take π as 3.14 and we get;
A = 3.14 X [tex] (100)^{2} / 4 [/tex]
Soving we get;
A = 7850 μ[tex]m^{2}[/tex]
Here we have to calculate the amount of dye molecules which will be needed for 10 fluorescent molecules / μ[tex]m^{2}[/tex] but;
here 1 μ[tex]m^{2}[/tex] = 7850 μ[tex]m^{2}[/tex] dye molecules.
Therefore, 10 fluorescent molecules will need;
7850 X 10 = 78500 molecules of dye.
Therefore, the answer is 78500 molecules of dye.