What to use for the Uncertainty

[Patricia Sourinphoumy Dis1C]

Hi! This might be a silly question, but I was wondering if someone could clear this up for me a bit.

I understand the concept of the Heisenberg Indeterminacy Equation, but for the actual delta p and delta x, I'm not entirely sure what is okay to input based on values given in the equation. Here is what I mean:

My understanding is that delta typically means "change" in general. So this is like a...range? So if the value was 10 plus or minus 2, the indeterminacy would be 4?

Why is it that the example given of the incorrect atomic model where "the electron is then confined to its nuclear diameter" uses the diameter as the uncertainty in position? Does the diameter count as the range? How do I know when to find the range myself?

[Sidney Shah 3H]

You are exactly right for change, so in your example of a value of 10, call it a velocity of 10 m/s, and you were given that it was within a range of +/- 2m/s, your value you would plug in for delta v would be 4. In this example, this wouldn't be equal to delta p, you would just now multiply 4*mass to get that delta p.
For the diameter question, we use the diameter because if you think about the maximum possible distance the electron could exist in that model, it would be the diameter.

[Emaad Sohail 3F]

It's not a silly question, I had the same problem, lol. Essentially you use the full range the uncertainty could be- if the uncertainty is the full atom, and it gives you the radius, you double it, because the diameter is the full range. If you have an uncertainty in velocity of plus or minus 10 m/s, for example, the uncertainty you use is 20.

[Harsimer Bal 3K]

Hi! I was also a bit confused on this topic but you are absolutely right! Delta v and Delta x are the change in velocity and position respectively, not the actual velocity and position so when solving for either one, you use the possible range of values. In your example, the indeterminacy would be 4 as you said because of the + or - 2 which creates a range of 4. In the example of the incorrect atomic model, the diameter is used as the uncertainty in position because the electron could be anywhere in the nucleus so the range of its position is the diameter of the nucleus, not the radius. You will know to find the range whenever radius is given (in which case you simply multiply by 2 to get the diameter) or if the problem gives a +- value for speed or position.