Answer:
b. [tex]3.313\times 10^{-16}\ m/s[/tex]
Explanation:
h = Planck's constant = [tex]6.626\times 10^{-34}\ m^2kg/s[/tex]
m = Mass of bacterium = [tex]10^{-14}\ kg[/tex]
L = Gap = 0.1 mm
Energy of a particle moving in a one dimensional box is given by
[tex]E=\dfrac{n^2h^2}{8mL^2}\\\Rightarrow E=\dfrac{1^2\times (6.626\times 10^{-34})^2}{8\times 10^{-14}\times (0.1\times 10^{-3})^2}\\\Rightarrow E=5.48798\times 10^{-46}\ J[/tex]
Kinetic energy is given by
[tex]K=\dfrac{1}{2}mv^2\\\Rightarrow E=\dfrac{1}{2}mv^2\\\Rightarrow v=\sqrt{\dfrac{2E}{m}}\\\Rightarrow v=\sqrt{\dfrac{2\times 5.48798\times 10^{-46}}{10^{-14}}}\\\Rightarrow v=3.313\times 10^{-16}\ m/s[/tex]
The minumum speed is [tex]3.313\times 10^{-16}\ m/s[/tex]
