## 6th Edition, 1.43

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

Alma Carrera 3C
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### 6th Edition, 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 a length equal to the diameter of the actual atom.

Can someone explain to me what steps they took when solving for this problem please? I'm very confused as to how it was solved in the solutions manual.

Chem_Mod
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### Re: 6th Edition, 1.43

You want to think about the Heisenberg Uncertainty Principle: △p△x ≥ h/4π. Because you are given uncertainty in velocity, we have to manipulate the equation so that we can find the uncertainty in velocity. Momentum by definition is mass times velocity. Because we know the mass of an electron, any uncertainty in momentum is reflected in the uncertainty in velocity. Thus, △p = m△v. △x is determined by the diameter of the atom, which represents the space where an electron could occupy. You then plug in your values, find the uncertainty in momentum, then calculate the uncertainty in velocity. Try this out, and see if it makes sense.