textbook 1B.5

[Catherine Bubser 2C]

Could someone explain why delta v is multiplied by 2 in part A of this example? The denominator as a whole is also multiplied by 2 because of the proportions so I'm confused as to why the uncertainty in the speed has to be multiplied additionally.

[Yasmina Zaarour 1G]

For the right side of the Heisenberg equation, they used h bar/2 instead of h/4pi. H bar is h/2pi, so either expression works. Sometimes, people use hbar because it is a simplified version of the equation.

[Melis Kasaba 2B]

The problem says the speed is known to within +/– 1.0 mm/s. This means that the range of possible values (delta v) would be twice that. For example, if the speed was 100 mm/s and it was known within +/– 1.0 mm/s, it could range from 99 mm/s to 101 mm/s, with a difference of 2.0. The 10^–3 comes from converting mm/s to m/s, and then that number has to be multiplied by 2.0 to account for the + 1.0 m/s value and the –1 m/s value.