A molecule of mass 2.0×10-24Kg is moving along at a speed of 100±10 m/sec, where the...

A molecule of mass 2.0×10^-24Kg is moving along at a speed of 100±10 m/sec, where the ±10 m/sec is the statistical spread or uncertainty in the determination of its velocity or ∆v = 10 m/sec. The molecule is somewhat localized in space and is described by a travelling wave packet solution to the Schrödinger equation centered around x=0 at t=0 and moving in the positive x-direction.

What is the minimum statistical spread or uncertainty ∆x in the determination of its position?
What is the de Broglie wavelength of this molecule?
Determine the frequency f of this travelling wave packet.
Does the frequency f in part d) satisfy the relation λf = v with the given central value of v=100 m/s? Show your calculation.
Suppose this electron has a wavefunction given at time t=0 by Ψ(x,0) = Asin((2π/λ)x). What is the probability density at x=λ/4? (Write your answer in terms of A and λ.)

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genius_generous answered 1 year ago

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