Problem: An electron has an uncertainty in its position of 190 pm. What is its uncertainty in its velocity?272 x 103 m/s 1.12 x 105 m/s 521 x 105 m/s 4.21 x 102 m/s 305 x 103 m/s

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FREE Expert Solution

We’re being asked to determine the uncertainty in the velocity of an electron with uncertainty in the position of 190 pm.

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)

Recall that momentum is expressed as:

$\mathbf{p}\mathbf{=}\mathbf{mv}$

where:

m = mass

v = velocity

Since the mass of an electron is constant, only its velocity can be uncertain

This gives us:

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

where:

m = mass (in kg)

Δv = uncertainty in velocity (in m/s)

Problem Details

An electron has an uncertainty in its position of 190 pm. What is its uncertainty in its velocity?

1. 272 x 103 m/s

2. 1.12 x 105 m/s

3. 521 x 105 m/s

4. 4.21 x 102 m/s

5. 305 x 103 m/s

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.

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