Chemistry Practice Problems Heisenberg Uncertainty Principle Practice Problems Solution: In the television series  Star Trek, the transport...

Solution: In the television series  Star Trek, the transporter beam is a device used to "beam down" people from the  Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a "Heisenberg compensator" into the transporter beam mechanism.Explain why such a compensator would be necessary to get around Heisenberg's uncertainty principle.

Problem

In the television series  Star Trek, the transporter beam is a device used to "beam down" people from the  Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a "Heisenberg compensator" into the transporter beam mechanism.

Explain why such a compensator would be necessary to get around Heisenberg's uncertainty principle.

Solution

We are asked to explain why a Heisenberg compensator would be necessary to get around Heisenberg's uncertainty principle in the Star Trek transporter.

Recall that Heisenberg’s Uncertainty Principle states that we cannot accurately determine both the position and velocity of an electron. This means we can only know either one at any given time


Mathematically, this is expressed as:


Δx·Δph4π


where:

h = Planck’s constant (6.626 × 10–34 kg • m2/s)

Δx = uncertainty in position (in m)

Δp = uncertainty in momentum (in kg • m/s)


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