00:01
Okay, so this question first tells us what this value planck's constant or h is.
00:08
And then it has two parts.
00:10
So the first part is asking us to figure out if we know the uncertainty in its position, we want to find the uncertainty in its momentum.
00:19
And this is heisenberg's uncertainty principle, which is a formula that states the uncertainty in its position times the uncertainty in its momentum is, has to be greater than or equal to this term, h bar over two.
00:34
So first let's figure out h bar is equal to h planks constant over 2 pi.
00:46
Sorry for the slanted writing there.
00:51
And we can solve for this since we have h.
00:55
And this is going to be equal to 1 .054.
01:04
6 times 10 to the negative 34th approximately.
01:09
Oh, boy.
01:14
Let's see if i'm in there.
01:17
Sorry, that's a little cramped.
01:20
And now that we have this, we're able to say, reduce this formula, say, delta x.
01:27
Or actually, we want to solve for delta p, right? the uncertainty in this momentum.
01:31
And we can solve for this by dividing by x on both sides, or dividing by delta x on both sides.
01:35
So delta p is going to be greater than equal to h bar over 2 times.
01:42
Times 1 over our delta x.
01:45
And for our purposes here, we can change this greater than or equal to to just be equal to.
01:55
Technically it would be greater than or equal to, but its uncertainty is going to be whatever that smallest value possible is.
02:03
And so here we can plug in our numbers and say 1 .0546 times 10 to the negative 34th over.
02:16
2 times 1 over 0 .0140...