Uncertainty Principle Question

In summary, the conversation discusses the ability to design lasers that emit pulses of light smaller than 30 microns wide in their direction of motion. The uncertainty in the momentum of a photon in such a pulse is estimated using the equation ΔxΔp ≥ h/4π, and the uncertainty in the wavelength of a photon is estimated using p = h/λ. By plugging in the values, it is determined that the uncertainty in momentum is 1.757 * 10-30 kg*m/s and the uncertainty in wavelength is 0.000377 m. The method used to calculate these values is also explained.
  • #1
lee_sarah76
18
0

Homework Statement



Laser can now be designed to emit pulses of light smaller than 30 microns wide
in their direction of motion.

(a) Estimate the uncertainty in the momentum of a
photon in such a pulse.

(b) The momentum of a photon is p=h/λ. Estimate the
uncertainty in the wavelength of a photon in the pulse, assuming a nominal
wavelength of 800 nm.


Homework Equations



ΔxΔp ≥ h/4π, p = h/λ

h being Planck's constant of 6.626 * 10-34 J*s

The Attempt at a Solution



My confusion with this problem stems from the fact that I'm not sure if Δx = 30*10-6m

If that is the case, then I did Δp ≥ h/4π*Δx.

Part a: Δp ≥ 1.757 * 10-30 kg*m/s

For part b, I then took the Δp value of 1.757 * 10-30 kg*m/s and plugged it into p = h/λ. I then got λ = 0.000377 m.

Is this the right method?
 
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  • #2
Seems good.
 

1. What is the Uncertainty Principle?

The Uncertainty Principle, also known as the Heisenberg Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to know both the position and momentum of a particle with absolute certainty at the same time. This means that the more accurately we know the position of a particle, the less accurately we can know its momentum, and vice versa.

2. Who discovered the Uncertainty Principle?

The Uncertainty Principle was first proposed by German physicist Werner Heisenberg in 1927. Heisenberg's work on the Uncertainty Principle is considered one of the most significant contributions to the development of quantum mechanics.

3. What is the significance of the Uncertainty Principle?

The Uncertainty Principle has significant implications for our understanding of the behavior of particles at the quantum level. It shows that there are fundamental limits to what we can know about the physical world and that the act of measurement itself can affect the system being observed.

4. How does the Uncertainty Principle relate to everyday life?

The Uncertainty Principle is not directly applicable to everyday life as it only applies to particles at the quantum level. However, it has led to advancements in technology such as the development of electron microscopes and lasers, which rely on the principles of quantum mechanics.

5. Is the Uncertainty Principle universally accepted?

Yes, the Uncertainty Principle is a widely accepted principle in physics and is supported by a vast amount of experimental evidence. It is considered one of the foundational principles of quantum mechanics and has been successfully used to explain many phenomena in the quantum world.

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