You want to confine an electron and you want to know for certain that the electron's speed is no more than 66 m/s.What is the length of the smallest box in which you can do this? A)5.5 × 10^-6 m B)1.1 × 10^-5 m C)2.8 × 10^-6 m D)1.4 × 10^-6m

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Quizplus · Accepted Answer

The de Broglie wavelength of the electron must be greater than the length of the box. The de Broglie wavelength is given by h/p, where h is Planck's constant and p is the momentum of the electron. The momentum of the electron is mv, where m is the mass of the electron and v is its speed. So, the de Broglie wavelength is h/mv. We want the de Broglie wavelength to be greater than the length of the box, so we have h/mv > L. Solving for L, we get L < h/mv. Plugging in the values for h, m, and v, we get L < 5.5 × 10^-6 m.

You Want to Confine an Electron and You Want to Know