Problem 1.43

[Ania Chavez Dis 4D]

(Problem 1.43) What is the minimum uncertainty in the speed of an electron confined to within a lead atom of diameter 350. pm? Model the atom as a one-dimensional box with length equal to the diameter of the actual atom.

In the problem is h a constant? I don't understand why we need to solve for h.

[2c_britneyly]

You would be solving for the uncertainty in velocity. h is a constant. 350 pm would be delta x, or the uncertainty in position.

[Anusha 1H]

You would use the Heisenberg principle in this problem.
350 pm is your uncertainty in position (delta x)
Because the problem is asking for uncertainty in velocity, we have to use (m)(delta v) as opposed to its equivalent delta p
The m is the mass of an electron or 9.11 x 10^31 kg.

h is always the constant in this equation. You can either use (h bar)/2 or h/4pi
When you rearrange the equation you get: delta v = h/ (4pi x m x delta x)
Hope that helps!