00:01
In this problem, we have to compare the uncertainties in the velocities of an electron as well as a proton, provided that these two particles are present in a box which is having length of one nanometers.
00:18
So basically, then certainty in the position will be equal to 10 raise to minus 9 because 1 nanometer is 10 raised to minus 9 meters.
00:28
And when we talk about the proton and an electron separately, we're going to determine the range of the velocities.
00:38
So first, we take the mass of the proton, which is approximately 1 .67 into 10 raised to minus 27 kilograms.
00:46
And the mass of an electron, on the other hand, that's 9 .31 into 10 raise to minus 31 kilograms.
00:53
And we use heisenberg's uncertainty principle to compute the uncertainty in the velocities.
01:00
And according to heisenberg's uncertainty principle, uncertainty in the momentum times the uncertainty in the position, that is equal to the planck's constant divided by 2 pi here.
01:12
So in this case, we take the value of the planx constant as 6 .6 to 6 x .26 into 10 raise to minus 34, 2 second approximately...