7th Edition Example 1B.5 (Page19)

[Diane Kang 2F]

For question (a) the question asks to estimate the minimum uncertainty in the position of a marble of mass 1.0g given that its speed is known to within +/- 1.00 mm s-1.

In the evaluation of the question, the textbook gives dx = (1.05457 * 10^-34 J s) / (2 * (1.0 * 10^-3 kg) * (2 * 1.0 * 10^-3 m/s)
Is there a reason why change in velocity dv is multiplied by 2, why does dv = (2 x 1.00x10^-3 m s-1) ?

[Katie Sy 1L]

The book is using the Heisenberg equation that is h with a dash over 2pi so that's why it's being multiplied by 2. I believe so?

[Diane Kang 2F]

h with a dash over 2p is already accounted for in the denominator in the equation: uncertainty in x = (1.05457 * 10^-34 J s) / (2 * (1.0 * 10^-3 kg) * (2 * 1.0 * 10^-3 m/s) )

But the textbook multiplies an extra 2 to uncertainty in velocity: (2 x 1.0 x 10^-3 m/s).