The de Broglie wavelength

In summary, the de Broglie wavelength is a concept in quantum mechanics that describes the wavelength associated with a moving particle. It can be calculated using the equation λ = h/mv, and it shows that all particles have wave-like properties. This concept is related to the Heisenberg uncertainty principle, and can be observed in everyday objects, although it is typically too small to be detected.
  • #1
plstevens
18
0
The mass of an electron is 9.11*10^-31 kg. If the de Broglie wavelength for an electron in an hydrogen atom is 3.31*10^-10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00*10^8 m/s.

here's what I did: i solved for velocity=6.626*10^-34J/(9.11*10^-31kg)(3.31*10^-10)
v=2.1974*10^-74
and i tried to gain the percent by dividing the speed of light by velocity.

where did i go wrong?
 
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  • #2
Your calculation is wrong. Don't just blindly do calculations. Think...does the number your calculator has spewed out actually make any sense? When it's something ridiculous like 10^-74 m/s, the answer is emphatically NO. Kind of slow for a particle, don't you think?

I get v = (0.00732)c
 
  • #3
plstevens said:
The mass of an electron is 9.11*10^-31 kg. If the de Broglie wavelength for an electron in an hydrogen atom is 3.31*10^-10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00*10^8 m/s.

here's what I did: i solved for velocity=6.626*10^-34J/(9.11*10^-31kg)(3.31*10^-10)
v=2.1974*10^-74
and i tried to gain the percent by dividing the speed of light by velocity.

where did i go wrong?


how did u calculate... watch the exponents first...

the magnitude is 10^7 m/s...

[tex]\frac{6}{9\times3}\times\frac{10^{-34}}{10^{-31}\times10^{-10}}\approx\frac{2}{9}10^7 m/s[/tex]
this suggest us that it is better to treat the electron relativistically if we want to penetrate deep in its properties...
regards
marco
 
  • #4
thanx Dirac :)
 
  • #5
so hows do i get the percentage here's what I'm doing: 3.00*10^8 m/s /100 = 0.00732/x. x=2.4*10^8, but i know this isn't right so, what shall i do?
 
  • #6
I'm not sure what percentage you are talking about, since it's not mentioned in the original post.

For the velocity of the particle, I get:

[tex] v = 2.197 \times 10^6 \ \ \ \frac{\textrm{m}}{\textrm{s}} [/tex]

The question asks how fast the particle is moving relative to the speed of light. Well, their ratio is

[tex] \frac{v}{c} = \frac{2.197 \times 10^6 \ \ \ \textrm{m/s}}{3.00 \times 10^8 \ \ \ \textrm{m/s}} = 0.00732 [/tex]

So, expressed in units of the speed of light, the velocity is

[tex] v = 0.00732c [/tex]

The particle is moving at 0.00732 times the speed of light. Obviously, as a percentage, that's 0.732%. So I guess if you wanted to, you could say that the particle is moving at 0.732% of the speed of light. It's a completely equivalent statement though. It doesn't add any extra meaning.
 

What is the de Broglie wavelength?

The de Broglie wavelength is a concept in quantum mechanics that describes the wavelength associated with a moving particle. It is named after French physicist Louis de Broglie.

How is the de Broglie wavelength calculated?

The de Broglie wavelength 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 its velocity.

What is the significance of the de Broglie wavelength?

The de Broglie wavelength is significant because it shows that all particles, including matter, have wave-like properties. This concept is a key aspect of quantum mechanics and helps explain the behavior of particles at the subatomic level.

How does the de Broglie wavelength relate to the Heisenberg uncertainty principle?

The de Broglie wavelength is related to the Heisenberg uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is because the de Broglie wavelength and momentum are inversely proportional, meaning that the more accurately we know the momentum of a particle, the less accurately we know its position.

Can the de Broglie wavelength be observed in everyday objects?

Yes, the de Broglie wavelength can be observed in everyday objects, but it is typically too small to be detected. However, in certain experiments, such as the double-slit experiment, the wave-like behavior of particles can be observed, including the de Broglie wavelength. This shows that the concept applies not just to subatomic particles, but to all matter.

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