a) Derive an expression for the de Broglie wavelength of an electron in the Bohr model...

a) Derive an expression for the de Broglie wavelength of an electron in the Bohr model of the hydrogen atom as a function of a0 and n.

b) Assume the uncertainty of the electron’s position is the diameter of its Bohr orbit. Derive an expression for the minimum uncertainty in electron’s velocity, (∆vn) as function of a0 and n (and other constants).

c) Use quantization of angular momentum to write an expression for the velocity as a function of n, vn . Then find an expression for the fractional uncertainty in the velocity (∆vn) /vn,, as a function of n. Finally, plug in your expression to fi nd the % uncertainty in the velocity for n=2.

Expert Solution

genius_generous answered 2 years ago

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