Question

A tiny bacterium with a mass of 10-14 kg is confined between two rigid walls 0.1 mm apart. Its minimum speed is:______a. 3.3 x 10^-14 m/s b. 3.3 × 10^-16m/s c. 2.6× 10^-14 m/s d. 1.3×10^-14 m/s e. 1.3 x 10^-16 m/s

Answer 1

b.
`3.313* 10^(-16)\ m/s`

Step-by-step explanation:

h = Planck's constant =
`6.626* 10^(-34)\ m^2kg/s`

m = Mass of bacterium =
`10^(-14)\ kg`

L = Gap = 0.1 mm

Energy of a particle moving in a one dimensional box is given by

`E=(n^2h^2)/(8mL^2)\\\Rightarrow E=(1^2* (6.626* 10^(-34))^2)/(8* 10^(-14)* (0.1* 10^(-3))^2)\\\Rightarrow E=5.48798* 10^(-46)\ J`

Kinetic energy is given by

`K=(1)/(2)mv^2\\\Rightarrow E=(1)/(2)mv^2\\\Rightarrow v=\sqrt{(2E)/(m)}\\\Rightarrow v=\sqrt{(2* 5.48798* 10^(-46))/(10^(-14))}\\\Rightarrow v=3.313* 10^(-16)\ m/s`

The minumum speed is
`3.313* 10^(-16)\ m/s`