Heisenberg Uncertainy Principle

In summary, modern electron microscopes in biological research emit a beam of electrons with a velocity of 1.5x108 m/s. The wavelength of an electron in the beam is 4.8494*10^-12m. The maximum acceptable uncertainty in the momentum of the electrons, according to the uncertainty principle, is 5.27*10^-25 kg*ms^-1.
  • #1
Dars
13
0

Homework Statement


Modern electron microscopes used in biological research emit a beam of electrons with a
velocity of 1.5x108 m/s
a. What is the wavelength of an electron in the beam?
b. The wavelength of the particle determines the resolution of the microscopy. Assume
that you desire a minimum uncertainty in electron position of 1A. Using the uncertainty
principle, what is the maximum acceptable uncertainty in the momentum of the
electrons?

Homework Equations



lamda = h/mv
p_0 = h/(4pi*delta x)

The Attempt at a Solution



a) lamda = h/mv = 4.8494*10^-12m

b) p_0 = h/(4pi*delta x) = 5.27*10^-25 kg*ms^-1? thanks
 
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  • #2
a) is not Heisenbergs uncertainty principle, this is de broglie wavelength

b) is "1A" one "angstrom" 10-10m?
 

What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the precise position and momentum of a particle. This means that the more accurately we know the position of a particle, the less we can know about its momentum, and vice versa.

Who came up with the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle was first proposed by German physicist Werner Heisenberg in 1927.

What is the significance of the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle has significant implications for our understanding of the behavior of particles at the quantum level. It suggests that there are inherent limits to what we can know about the physical world, and that particles do not have definite properties until they are measured.

How does the Heisenberg Uncertainty Principle relate to the wave-particle duality of particles?

The Heisenberg Uncertainty Principle is closely related to the wave-particle duality of particles, which is the idea that particles can exhibit both wave-like and particle-like behavior. This principle suggests that the position and momentum of a particle cannot both be known precisely because particles can behave like waves, which do not have a well-defined position.

Is the Heisenberg Uncertainty Principle a fundamental law of nature?

Yes, the Heisenberg Uncertainty Principle is considered to be a fundamental law of nature and is supported by numerous experimental observations. It is a cornerstone of quantum mechanics and is used to explain many phenomena at the quantum level.

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