Calculating de Broglie Wavelength & Double-Slit Fringe Width

In summary, the de Broglie wavelength for an electron with v=0.001c is 2.42x10^-9m. To find the angular width of the central bright fringe in a double slit experiment with a separation of d=50nm, the equation d*sin(theta)=n*wavelength can be used, where theta represents the angle between the first-order minima. It is important to note that this is an interference pattern, not a diffraction pattern, and the distance from the screen to the source is not needed for this calculation.
  • #1
v_pino
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Homework Statement


Find the de Broglie wavelength for an electron with v=0.001c. Find the angular width of the central bright fringe in a double slit experiment, with the separation of the two slits d=50nm.


Homework Equations



wavelength = h/mv

d sin(theta)=n*wavelength

The Attempt at a Solution



For the wavelength, I got 2.42x10^-9m. I think this sounds correct.

Is my second equation for diffraction applicable here? I know that it is double slits so there will be interference and not just diffraction. If this equation is applicable, the my answer is 2*theta = 5.55 degrees.

Or is there a specific equation for double slit that I should use?
 
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  • #2
How can you calculate anything about diffraction without knowing the slit size?
 
  • #3
So does it mean that the question is just asking for the angle to the first maximum as in that of a diffraction pattern using dsin(theta) = n*wavelength?
 
  • #4
Not exactly. You want to find the angle between the first-order minima, since they border the central maximum.
 
  • #5
Sorry for not understanding the simplest of the idea here. So are you saying that the diffraction equation can be used in the question even though it is asking for interference? If so, the answer should simply be 2*theta with theta being from the equation d*sin(theta)=n*wavelength?
 
  • #6
Where did I say to use the diffraction equation?
 
  • #7
I don't get where you are trying to lead me here. Am I missing a big clue? Should I be using some sort of approximations? Plus I don't know the distance from screen to source - should I be estimating this?
 
  • #8
What does "angular width of the central bright fringe" mean?
 

1. What is the de Broglie wavelength and how is it calculated?

The de Broglie wavelength is the wavelength associated with a particle moving at a certain velocity. It can be calculated using the equation λ = h/mv, where λ is the de Broglie wavelength, h is Planck's constant, m is the mass of the particle, and v is the velocity of the particle. This equation is based on the concept of wave-particle duality, which states that all matter has both wave-like and particle-like properties.

2. How does the double-slit experiment demonstrate the wave-like behavior of particles?

The double-slit experiment involves firing particles, such as electrons, through two parallel slits onto a screen. When only one slit is open, the particles create a simple pattern on the screen. However, when both slits are open, the particles create an interference pattern, similar to what is seen with waves. This demonstrates the wave-like behavior of particles, as they are able to interfere with each other and create a pattern.

3. What is the significance of the double-slit fringe width?

The double-slit fringe width is the distance between two adjacent bright fringes in the interference pattern created by the double-slit experiment. It is a measure of the spacing between the particles as they interfere with each other. This width can be used to calculate the de Broglie wavelength of the particles, providing insight into their wave-like behavior.

4. How does the mass and velocity of a particle affect its de Broglie wavelength?

According to the de Broglie equation, the de Broglie wavelength is inversely proportional to the mass and directly proportional to the velocity of a particle. This means that lighter particles and faster-moving particles will have shorter de Broglie wavelengths, while heavier particles and slower-moving particles will have longer de Broglie wavelengths.

5. Can the de Broglie wavelength and double-slit fringe width be applied to macroscopic objects?

The de Broglie wavelength and double-slit fringe width are primarily applicable to microscopic particles, such as electrons, due to their small mass and high velocity. While these concepts can technically be applied to macroscopic objects, the wavelengths and fringe widths would be immeasurably small and difficult to observe. Therefore, they are typically only used to describe the behavior of particles at the atomic and subatomic level.

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