## Example 1.7

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Gabi Landes 1-H
Posts: 31
Joined: Thu Feb 22, 2018 3:00 am

### Example 1.7

Hello!
In text example 1.7 (p. 18) -

Estimate the minimum uncertainty in:
(a) the position of an object as heavy as a marble of mass 1.0 g given that its speed is known within +1.0mm/s and
(b) the speed of an electron confined to within the diameter of a typical atom (200. pm).

Why is $\Delta$v = 2 x (1.0x10^-3 m/s)?

I would think this would simply be 1.0x10^-3 m/s because the "speed is known within +1.0mm/s" not +2.0mm/s?

annie_finneran_1K
Posts: 37
Joined: Fri Apr 06, 2018 11:02 am

### Re: Example 1.7

because its +or- 1 it is really 2 because it is either plus 1 or minus 1 so the overall range is actually 2. does that make sense? like if a dog's weight fluctuated around 50 lbs with +-1, then its weight is either 49,50,or 51 lbs, but the overall range in the uncertainty of its weight at a time is actually 2 lbs.

Daniel Cho Section 1H
Posts: 29
Joined: Fri Jun 23, 2017 11:40 am

### Re: Example 1.7

A better way to look at the indeterminacy of the velocity is to find the values of whatever speed you are given plus and minus a random number. For example, plus minus 1 is doubled because you are subtracting the range which would lead to 1 and -1 mm/s. When you subtract 1 and -1 you would get 2 which is double your given velocity.

Another example is 133[+][/u] .5. 133+.5 is 133.5 as 133-.5 is 132.5. When you subtract 133.5-132.5, the difference is 1.

I hope this helps as a good way to figure out why we double the velocity as a good shortcut to finding the indeterminate velocity.