heisenberg module #18

[StephanieIb]

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.

How would I go about solving this? I know how to use the equation but i think the radius and 1% is throwing me off. Thank you

[John Pham 3L]

For uncertainty in position, they tell you that it is 1% of the Hydrogen atom's radius.
To find this, just multiply 0.05 nm by 0.01 and convert to m for

Once you have this, plug it into the Heisenberg Indeterminacy equation and solve for
Remember that equals times mass of electron (9.11*10^-31 kg).
Solve for to get the uncertainty in the speed of the electron

[Tessa House 3A]

Since they give you the radius and say the uncertainty in position is 1% of this value, you can find uncertainty in position first. Convert 0.05 nm to m because these units are needed for later calculations. Then take 1% of this value by multiplying it by 0.01 to find the uncertainty in position. From there, you can use Heisenberg's indeterminacy principle to solve for delta p using delta x. Then, calculate delta v, uncertainty in speed, using delta p calculated before and the mass of an electron, a constant given to you. This is your answer.

[Asia Yamada 2B]

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.