00:01
Hi there.
00:02
So for this problem, we are told to estimate the kinetic energy of an electron that is confined within a nucleus of size that we're going to call this size.
00:13
Well, let's just call it delta x.
00:18
And that is equal to 1 times 10 to the minus 14 meters.
00:26
And this by using the uncertainty principle.
00:32
Now, we started with the uncertainty principle.
00:36
We noted that the product between the momentum and the position is equal to, well, the minimum is equal to plums constant divided by two times pi.
00:50
So if we solve for the uncertainty on the momentum, because with this, we are going to determine the kinetic energy because we know that the kinetic energy, is equal to the momentum squared divided by two times the mass.
01:07
So that's why we are doing this.
01:10
And this, then we will left with plums constant divided by two times pi times delta x, which in this case is going to be the radius of the nucleus.
01:22
Now, to obtain the momentum, we just simply substitute the numerical value.
01:28
So we will have in the denominator 2 times pi times 1 times, 10 to the minus 14 meters.
01:37
And in the numerator we have plans constant, which is 6 .63 times 10 to the minus 24 joules times seconds.
01:51
So using our calculator, we obtain, oh, sorry, in here it is 34.
02:00
6 .63 times 10 to the minus 34.
02:09
And that divided by 2 times pi times 1 2 times 10 to the minus 14.
02:19
So from the calculator we obtain a value of 1 .055.
02:32
Times 10 to the minus 20 kilograms times meters per second...