Solution: 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

Solution: 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

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

- 272 x 10
^{3}m/s

- 1.12 x 10
^{5}m/s

- 521 x 10
^{5}m/s

- 4.21 x 10
^{2}m/s

- 305 x 10
^{3}m/s

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:

$\overline{){\mathbf{\Delta x}}{\mathbf{\xb7}}{\mathbf{\Delta p}}{\mathbf{\ge}}\frac{\mathbf{h}}{\mathbf{4}\mathbf{\pi}}}$

where:

**h** = Planck’s constant (6.626 × 10^{–34} kg • m^{2}/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:

$\overline{){\mathbf{\Delta x}}{\mathbf{\xb7}}{\mathbf{m\Delta v}}{\mathbf{\ge}}\frac{\mathbf{h}}{\mathbf{4}\mathbf{\pi}}}$

where:

**m** = mass (in kg)

**Δv** = uncertainty in velocity (in m/s)