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What does << mean?
Transcribed Image Text:What does << mean?
According to de Broglie's particle-wave duality formula, the momentum of a particle is related to its wavelength as: p = *. If the wavelength is A, + AA, where Al is the uncertainty, what is the uncertainty in the momentum of the particle? You can assume that JA|/1, << 1. Derive a formula for the uncertainty in momentum that keeps track of the sign of A. If your measuring device for wavelength has a fixed resolution of Aa, explain how the error in momentum will increase or decrease depending on the wavelength measured. Discuss how the sign the uncertainty in wavelength affects the uncertainty in the momentum. Sketch a graph too.
Transcribed Image Text:According to de Broglie's particle-wave duality formula, the momentum of a particle is related to its wavelength as: p = *. If the wavelength is A, + AA, where Al is the uncertainty, what is the uncertainty in the momentum of the particle? You can assume that JA|/1, << 1. Derive a formula for the uncertainty in momentum that keeps track of the sign of A. If your measuring device for wavelength has a fixed resolution of Aa, explain how the error in momentum will increase or decrease depending on the wavelength measured. Discuss how the sign the uncertainty in wavelength affects the uncertainty in the momentum. Sketch a graph too.
Expert Solution
Step 1

Given:

Momentum of the particle

 p=hλwhere λ is the wavelength.And  λ=λ0+∆λ

Uncertainty in Wavelength=∆λ

Explanation:

a)The sign << means "much much less".

 

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