Using Heisenberg’s uncertainty principle, calculate the uncertain...

Question

Using Heisenberg’s uncertainty principle, calculate the uncertainty
in the position of (b) a proton moving at a speed of 15.00 { 0.012 * 104 m/s.
(The mass of a proton is given in the table of fundamental
constants in the inside cover of the text.)

Accepted Answer

Hi everyone today, we have a question telling us using Heisenberg's uncertainty principle, calculate the approximate uncertainty in the position of an electron with the uncertainty in the speed of 4.8 times 10 to the third meters per second and it gives us the massive and electron there. So we're going to use Heisenberg's uncertainty principle formula. So that is delta X, which is our position times delta P, which is our momentum is greater than or equal to Plank's constant over four pi. So now let's plug in what we know. So our change in position Times are momentum, which is 4.8 Times 10 to the 3rd, meters per second is greater than or equal to Plank's constant, which is 6.6-6 Times 10 to the negative 34 kilograms times meter squared over seconds. And then that's divided by four pi. So let's go ahead and calculate that on the right there. So we'll end up with delta x times 4. Times 10 to the 3rd m/s is greater than or equal to five .273 Times 10 to the negative, 35 kilograms times meters squared per second. And now we're gonna go ahead and divide both sides by this 4.8 Times 10 to the negative or 10 to the third. And that's going to take away one of the meters and the second. So our position is going to equal or be greater than or equal to 1.09, 85 Times 10 to the negative kilograms times meters. Now, our position cannot be in meters cannot be in kilograms times meters. We need it to be in kilograms. So now what we're going to do is divide by Our mass of an electron so 9.11 Times 10 to the -31 kg. And that's going to take away our kilograms. And then we're gonna have our answer of our position Is greater than or equal to 1.2 times 10 To the -8 m. And that is our final answer. And it is the Thank you for watching. Bye.

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