Chemistry Practice Problems Heisenberg Uncertainty Principle Practice Problems Solution: According to the Heisenberg uncertainty principle,...

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# Solution: According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 x 103 m/s, the uncertainty in its position (in m) is at least.66 m 17 m 6.6 x 10-8 m 1.7 x 10-8 m 2.1 x 10-10 m

###### Problem

According to the Heisenberg uncertainty principle, if the uncertainty in the speed of an electron is 3.5 x 103 m/s, the uncertainty in its position (in m) is at least.

1. 66 m

2. 17 m

3. 6.6 x 10-8 m

4. 1.7 x 10-8 m

5. 2.1 x 10-10 m
###### Solution

We’re being asked to determine the uncertainty in the position of an electron with uncertainty in the speed of 3.5 × 103 m/s.

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:

$\overline{){\mathbf{\Delta x}}{\mathbf{·}}{\mathbf{\Delta p}}{\mathbf{\ge }}\frac{\mathbf{h}}{\mathbf{4}\mathbf{\pi }}}$

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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