Question about the Delta X and what it stands for

[Yu Jin Kwon 3L]

Hi guys! So I've been noticing that different problems give us the (for example) radius of the atom and others give us the uncertainty in the position of the electron within that atom. So, I wanted to ask: is delta X the distance of the area (like the length of the radius of an atom) or the uncertainty in position (like the +- 1%)? If they're the same thing, can someone elaborate on how they're the same thing?

[Astha Patel 2J]

Delta X refers to uncertainty in position. In a problem where they say that the electron is bound by an atom, the uncertainty of the position would be the length of the atom because the electron could be anywhere in that range. If the problem said something like the uncertainty was 10 nm +/- 2nm, then the delta x would be the difference between the range of possible positions:

10-2=8 to 10+2 = 12
So the uncertainty in position would be 12-8 = 4

[Gina Spagarino 3G]

From another example, delta x was found using a given uncertainty in momentum (ex "speed is known within +/- 1.00 mm/s), without giving a specific +- for the delta x because the delta x value can be solved using the equation (delta p)(delta x) is greater than or equal to h/4pi... in the example in the lecture with the incorrect atomic model, we used the nuclear diameter (1.7 x 10^-15 m) as the delta x value because the problem stated the electron could be contained anywhere in the diameter. So I think the value to use for delta x depends on whether you are given the uncertainty with a + or -, or with phrasing along the lines of "can be contained within".

[Mackenzie Stockton 2H]

When it says delta x is equal to 10 m/s + or - 3, then the uncertainty in x would be 6

when it says delta x is 1% of the radius (or anything along these lines), take 1% of the specified value

When an electron or something is confined to the atom, the uncertainty is the diameter of the atom

[Mackenzie Van Val 3E]

Hi! To echo what the other commenters have said, delta X stands for the uncertainty in position. There are many different ways this uncertainty can be shown. If the diameter of the electron's "container" is given, then that will be the uncertainty in position. For example, in a problem that we did yesterday in Justin's workshop, the diameter of quantum dot that the electron was in was 9.25 nm; therefore, delta X=9.25 nm. A problem may also say that the uncertainty is 2% of the given measurement. In this case, if the measurement was 9 m, then you would take 2% of 9 m to find the uncertainty (which would be 0.18 m). Therefore, the electron's position could be between 8.82 m and 9.18 m. I hope this helps!

[Reese_Gover2K]

Delta x is in fact the uncertainty of position. So if the radius given is 6 and the uncertainty is +-1 then you would do the math (6-1=5, 6+1=7, 7-5=2) to get the uncertainty of position is 2. If they tell you the electron or particle is confined to the atom, the uncertainty of position would be the diameter of the atom.

[Alejandro Gonzalez 2G]

I believe Delta X refers to the uncertainty in position, like how delta v stands for uncertainty in velocity.