## Heisenberg Uncertainty Principle Post Assessment Q#18

$\Delta p \Delta x\geq \frac{h}{4\pi }$

IsabelMurillo3J
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### Heisenberg Uncertainty Principle Post Assessment Q#18

The hydrogen atom has a radius of approximately 0.05 nm. Assume that we know the position of an electron to an accuracy of 1 % of the hydrogen radius, calculate the uncertainty in the speed of the electron using the Heisenberg uncertainty principle.
Does anyone know the steps I have to take to solve this problem? Specifically on how to get the values of delta p and delta x? Thanks in advance!

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### Re: Heisenberg Uncertainty Principle Post Assessment Q#18

Step 1) I like to first determine what variable I need to solve for. We are looking for the uncertainty in the speed of the electron, which is delta v.

Step 2) We are told that the uncertainty in the position of the electron is 1% of the hydrogen atom radius (0.05nm).

0.01 x 0.05 nm = 0.0005 nm

Convert this to meters because the unit for uncertainty in position is meters.

0.005 nm x (10^-9 m / 1nm) = 5 x 10^-13 m

Step 3) Since we are talking about an electron, the mass will be 9.11 x 10^-31 kg.

Step 4) Plug the values into the Heisenberg uncertainty equation:

$(9.11 x 10^{-31}) (\Delta V) \cdot (5x10^{-13}) \geq \frac{h}{4\pi }$

Delta v will be greater than or equal to 1 x 10^8 m/s

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### Re: Heisenberg Uncertainty Principle Post Assessment Q#18

First, you would convert the radius into meters which would be 5x10^-11m. You have to multiply the radius by 0.01 because the radius is known to an accuracy of 1%. You should get 5x10^-13m. This is the uncertainty in position and from there you can just plug the uncertainty in position into Heisenberg’s Indeterminacy Equation (Δx • Δp ≥ h/4pi). This will give you the uncertainty in momentum. Since p=mv, and you know the mass of an electron (9.109x10^-31kg), you can solve for uncertainty in velocity.

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