De Broglie wavelength, Maximum kinetic energy, and smoke particles

In summary, the conversation is about various physics problems, including estimating the mass of smoke particles, finding the de Broglie wavelength of a particle, and showing that Boyle's Law is obeyed in a small rectangular box with a piston. The participants are seeking help and discussing their attempts at solving the problems. The solution to the first problem involves using relativistic equations, while the second problem requires finding the smallest possible energy of a particle moving at right angles to a plane. The third problem involves applying Boyle's Law to a system of particles in a box with a changing length.
  • #1
Badrakhandama
25
0
I have a few questions:
1. 'small smoke particles in air are seen under a low magnification microscope to move randomly at a speed of 0.10mm/s. The speed of sound in air is 330m/s. Estimate the mass of the smoke particles.

I cannot make the link between speed of particle and speed of sound - I was thinking something to do with relativistic equations but none involve sound :confused:

2a) Show that the de Broglie wavelength, L, of a particle of mass m, moving at velocity v, where v<<c is related to the KE of the particle by:

L = h/((2mKE)^.5)

I have done this, however the next part i cannot get:

b) consider the particle in a small rectangular box with sides of length a, b and c. The particle is moving at right angles to the b-c plane. Find an expression for the smallest possible energy. (think about the amplitude of the wave at the wall of the box)


I thought: rearranging gives KE = h^2/(2mL^2)

then differentiate with respect to L, and set it equal to zero but it doesn't seem right to me!

c) the box now contains many particles, and one b-c plane of the box is replaced by a piston. Show that as the length, a, is SLOWLY decreased the resulting change in wavelength ensures that Boyle's Law is obeyed.

My attempt: pV = nRT, where T is constant. From here, I have no clue what to do.
 
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  • #2
Ok, i have done question 1 now

Any help with the other two would be colosally appreciated
 
  • #3
well you have to fit multiples of full wavelengths into the box so the lowest energy is L= a
 

Related to De Broglie wavelength, Maximum kinetic energy, and smoke particles

1. What is the De Broglie wavelength?

The De Broglie wavelength, named after French physicist Louis de Broglie, is a concept in quantum mechanics that relates the wavelength of a particle to its momentum. It is given by the equation λ = h/p, where λ is the De Broglie wavelength, h is Planck's constant, and p is the momentum of the particle.

2. How is the De Broglie wavelength related to the concept of wave-particle duality?

The De Broglie wavelength is a key concept in the wave-particle duality theory, which states that particles can exhibit both wave-like and particle-like properties. The De Broglie wavelength is used to describe the wave-like behavior of particles, while their momentum is used to describe their particle-like behavior.

3. What is the maximum kinetic energy of a particle?

The maximum kinetic energy of a particle is the maximum amount of energy that a particle can possess due to its motion. It is given by the equation Kmax = hν, where Kmax is the maximum kinetic energy, h is Planck's constant, and ν is the frequency of the particle's motion.

4. How does the maximum kinetic energy of a particle relate to its velocity?

The maximum kinetic energy of a particle is directly proportional to its velocity. This means that as the velocity of a particle increases, its maximum kinetic energy also increases. However, the relationship between the two is not linear, as the maximum kinetic energy also depends on the mass of the particle.

5. How are smoke particles able to exhibit both wave-like and particle-like properties?

Smoke particles, like all other particles, can exhibit wave-like and particle-like properties due to the wave-particle duality theory. However, the De Broglie wavelength of smoke particles is very small, making it difficult to observe their wave-like behavior. Additionally, smoke particles are constantly interacting with their surroundings, which can also affect their behavior and make it harder to observe their wave-like properties.

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