A spherical virus has a diameter of 50mm .
It is contained inside a long, narrow cell of length . 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.
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To determine the uncertainty in the velocity of the virus along the length of the cell, we need to use Heisenberg's uncertainty principle. This principle states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously.
The uncertainty principle is expressed as:
Δx * Δp ≥ h/4π
Where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant (h = 6.626 x 10^-34 J*s).
In this case, we are interested in the uncertainty in velocity. Velocity is defined as the change in position (length) over the change in time. Since we are given the diameter of the virus (50 mm), we can determine the uncertainty in position as half of this diameter (since it's a spherical virus), which is 25 mm.
Now, let's assume we want to find the uncertainty in velocity within a certain time interval, Δt, along the length of the cell. The uncertainty in velocity, Δv, can be expressed as:
Δv = Δx/Δt
Substituting the uncertainty in position, Δx = 25 mm, we have:
Δv = 25 mm/Δt
To find the uncertainty in velocity, we need to determine the time interval, Δt. Unfortunately, the length of the cell is not provided in the question, so we cannot determine the exact value of Δt.
Therefore, without knowing the length of the cell, we are unable to calculate the uncertainty in velocity along the length of the cell for the given spherical virus.