Midterm Question

[Cristian Carrasco 1F]

I know the formula to solve this but I'm confused on how to solve it ?

Find the uncertainty in the position of a marble of mass 1.5 g given that it’s speed is
known to within ± 0.55 m.s-1.

[Kevin Ru 1D]

As you know, Heisenberg's uncertainty principle is: Δp x Δx ≥ h/4π

Now, the question gives us the mass of the marble as well as the uncertainty in velocity which allows us to find Δp. Since momentum is mass x velocity, you take 1.5 x 10^-3 kg (converted from grams) x 1.1 m/s (because +/-). This will give you your Δp value. Simply divide the other side of the equation by Δp and you will have solved for Δx.

Hope that helps!

[Aijun Zhang 1D]

The point is that the uncertainty of velocity is 0.55 x2 = 1.1 m/s since it can be plus or minus 0.55. The range is actually larger.
momentum(p) = m * v.
uncertainty in momentum in this case = m * Δv.
so Δp = 0.55 * 2 * 1.5 * 10^-3 (you need to convert grams into standard unit kilograms)
The Heisenberg's uncertainty principle is: Δp x Δx ≥ h/4π. So the equation becomes 0.55 * 2 * 1.5 * 10^-3 * Δx ≥ h/4π.
With h and π are constants, you then can calculate Δp.
The answer is 3.2*10^-32 m.