Use the Heisenberg uncertainty principle to calculate the uncerta...

Question

Use the Heisenberg uncertainty principle to calculate the uncertainty in meters in the position of a honeybee weighing 0.68 g and traveling at a velocity of 0.85 m/s. Assume that the uncertainty in the velocity is 0.1 m/s.

Accepted Answer

everyone in this example, we have a seven kg pound dog running at a rate of 2.3 m per second. We need to identify the uncertainty and position of the dog. If its speed is measured with within point oh one m per second, we would recall that the uncertainty and position is represented by the symbol delta X. So we're going to utilize the following formula which we recall where uncertainty of position, Delta X should be greater than or equal to our plank's constant H, which is divided by four times pi times our uncertainty and momentum represented by delta P. So recall that uncertainty in momentum is in units of kilograms times meters per second. So based on the info on the prompt, we're going to find our uncertainty in position which is greater than or equal to Planck's constant, which we would plug in as 6.626 times 10 to the negative 34th power jewels, Time seconds in our numerator, This is divided by four times pi which is multiplied by our uncertainty in momentum delta P. So to get that we're going to take our massive our dog. So that was given in the pump as seven kg. And we're going to multiply it by the given velocity in the prompt, which is 0.01 m/s. And so as you can see, we've substituted the info from the prompt to get our uncertainty in momentum equal to seven kg times 0.01 m/s. So what we're going to get is that our uncertainty in position is going to be greater than or equal to a value of 7.53 to 6 times 10 to the negative 34th power. And this would be our final answer to complete this example as our uncertainty of position of our dog. In this example, if you have any questions, leave them down below and I'll see everyone in the next practice video.

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