Question

A spherical virus has a diameter of 60 nm. It is contained inside a long, narrow cell of length 1×10−4m1×10−4m. What uncertainty does this imply for the velocity of the virus along the length of the cell? Assume the virus has a density equal to that of water.

Answer 1

Given,

The diameter of the spherical virus, d = 60 n = 60 * 10^-9 m

So, the radius, r = 30 * 10^-9 m

The length of a narrow cell, L or x = 1 * 10^-4 m

The density of virus = The density of water, = 1000 Kg / m³

We know,

m = V

= * (4/3) * r³

= 1000 * (4/3) * * ( 30 * 10^-9)³

= 1.131 * 10^-19 Kg

By using Heisenberg's Uncertainity principle,

x * p = h / 4

x * m * v = (6.625 * 10^-34) / 4

1 * 10^-4 * 1.131 * 10^-19 * v = 5.273 * 10^-35

v = 4.66 * 10^-12 m/s