An electron has an uncertainty in its position of 552 pm. What
is...

Question

An electron has an uncertainty in its position of 552 pm. What
is the uncertainty in its velocity?

Accepted Answer

Hey everyone in this example, we need to calculate the uncertainty and velocity for neutron given the uncertainty in its position as 605 PICO meters. So we want to recall that our uncertainty in velocity is represented as delta V. We want to recall that our neutron has a specific mass. That is equal to 1.67 times 10 to the negative 27th power kg, which are the proper units for mass here. And we want to recall that the uncertainty and position is represented as delta X and should be in units of meters. So our first step is to actually take our given PICO meters. And we're going to convert from PICO meters in our denominator and into meters as our final unit. So we want to recall that our prefix PICO tells us that for one pick zero m we would have 10 to the negative 12 power meters. So this allows us to cancel our PICO meter units, leaving us with meters and this gives us our uncertainty and position as six point oh five times 10 to the negative 10th power meters, which are the proper units for our uncertainty in position. So our next step is to recall our formula for the Heisenberg uncertainty principle. And this is given as our uncertainty and position. Delta X multiplied by the mass of our object. M. And this should be in kilograms, which is then multiplied by our uncertainty and velocity delta V. And then this is greater than or equal to in our numerator, we have plank's constant on the right hand side divided by four times pi. So now that we have pretty much all of the given information, we can plug this into our formula. So what we would have is our uncertainty and position, which we just found as six point oh five times 10 to the negative 10th power meters. Multiplied by the mass of our object which in this case is our neutron. We recall that that mass is 1.67 times 10 to the negative 27th power kg. And then multiplied by our uncertainty and velocity delta v. This is then set greater than or equal to in our numerator. We should recall that Plank's constant is 6. times 10 to the negative 34th power. And we're going to recall that that's jewels times seconds In our denominator, we're just going to have four times pi. So we also want to recognize that we can simplify our units for plank's constant even further by recalling that jules is equal to kilograms times meters squared divided by seconds squared. And so what we can have instead, when we multiply the two quantities on our left hand side, we're going to have 1.103 times 10 to the negative 36 power kilograms times meters now. And this is multiplied by our uncertainty and velocity delta V set greater than or equal to what we would have in our numerator again is 6.626 times 10 to the negative 34th power plank's constant. And we're going to substitute our interpretation for jewels as kilograms times meters squared, divided by seconds squared. And this is still multiplied by seconds as it was here in our previous step. And so in our denominator we would still have four pi. So this allows us to actually cancel out that second in the denominator with the seconds over here and we can further simplify the right hand side in our next line. So our left hand side is still going to be 1.103 times 10 to the negative 36 power kilograms times meters multiplied by our uncertainty and velocity set greater than or equal to. We're going to actually take this whole quantity in our calculators here And this is going to give us a value that we simplify as 5.27- times 10 to the negative 35th power kilograms times meters squared. And then divided by just seconds. Now that we canceled our seconds out. And so now we want to isolate for our uncertainty and velocity delta V. And so on the left hand side, we're going to divide both sides by one point oh one oh three times 10 to the negative power kilograms times meters and also on the right hand side. So this allows us to cancel this unit on the left hand side as well as canceling out kilograms meters. So we're left with just meters per second as our final unit. And so this would give us in our calculators, our uncertainty of velocity set greater than or equal to on the right hand side. We should get 52.2 m per second and this is actually the appropriate amount of sick fix because based on the information given in our problem, we should only have minimum three sig figs. And so to complete this example, our uncertainty for the velocity of our neutron is equal to or sorry, greater than or equal to 52.2 m/s. So I hope that everything we reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity?

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