# 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.66 m 17 m 6.6 x 10-8 m 1.7 x 10-8 m 2.1 x 10-10 m

###### FREE Expert Solution
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###### FREE Expert 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)

85% (268 ratings)
###### Problem Details

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

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Heisenberg Uncertainty Principle concept. You can view video lessons to learn Heisenberg Uncertainty Principle. Or if you need more Heisenberg Uncertainty Principle practice, you can also practice Heisenberg Uncertainty Principle practice problems.

What is the difficulty of this problem?

Our tutors rated the difficulty ofAccording to the Heisenberg uncertainty principle, if the un...as medium difficulty.

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Based on our data, we think this problem is relevant for Professor Costanza's class at USF.