De Broglie wavelength, velocity of electron

In summary, the de Broglie wavelength of a neutron moving at one fiftieth of the speed of light is 2.64*10^-15 meters, and the velocity of an electron with a de Broglie wavelength of 225.7 pm is 3.22*10^6 meters per second. The equations used for these calculations are the wavelength of a particle equation and the Bohr model equation.
  • #1
Sublime74
3
0

Homework Statement



Question 1) Calculate the de Broglie wavelength of a neutron (mn = 1.67493×10-27 kg) moving at one fiftieth of the speed of light (c/50).


Question 2) Calculate the velocity of an electron (me = 9.10939×10-31 kg) having a de Broglie wavelength of 225.7 pm.


Homework Equations



Wavelength of a particle = Plancks constant/(mass)(velocity)
Plancks constant= 6.626068 x 10^-34
I know this, and it should be plug and chug but my answer is always wrong...any help would be greatly appreciated!

The Attempt at a Solution

 
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  • #2
I got..

1) 2.64*10^-15
2) 3.22*10^6 m/s

what did you get?
 
  • #3
Plug it into

nh/2(pi)m(e-)r(e-)

n= proton number
h= 6.62 x 10^-34
m= e- mass 9.11 x 10^-31 m
r= Bohr radius 5.2 x 10^-11 m
 

Related to De Broglie wavelength, velocity of electron

1. What is the De Broglie wavelength?

The De Broglie wavelength is a property that describes the wave-like nature of particles, specifically electrons. It is the wavelength associated with a moving particle and is inversely proportional to its momentum.

2. How is the De Broglie wavelength calculated?

The De Broglie wavelength can be calculated using the equation λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is the velocity of the particle.

3. What is the significance of the De Broglie wavelength?

The De Broglie wavelength is significant because it provided evidence for the wave-particle duality of matter, which states that particles can exhibit both wave-like and particle-like behavior. It also helped explain certain phenomena in quantum mechanics, such as the diffraction of electrons.

4. What is the relationship between De Broglie wavelength and velocity of an electron?

The De Broglie wavelength and velocity of an electron are inversely proportional. This means that as the velocity of an electron increases, its wavelength decreases, and vice versa.

5. Can the De Broglie wavelength be observed in everyday life?

No, the De Broglie wavelength is only applicable to objects at the quantum level, such as electrons. It is not observable in everyday life as it is too small to be detected without specialized equipment.

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