[Multiple Choice] wavelength of an object. de Broglie wavelength

In summary, the de Broglie wavelength of an object is the smallest wavelength that can be detected by conventional means.
  • #1
daNAV1GATOR
45
0
[SOLVED] [Multiple Choice] ...wavelength of an object. de Broglie wavelength

1. THE PROBLEM STATEMENT

MULTIPLE CHOICE
Which of the following would you expect to have the largest wavelength associated with it?

(A) a quick-moving bee
(B) an electron orbiting a nucleus
(C) a slowly lumbering elephant
(D) the Earth orbiting the sun
2. RELEVANT EQUATIONS

The wavelength of a particle is called the de Broglie wavelength.

wavelength = [tex]\frac{h}{momentum}[/tex]

h = Planck's constant
3. THE ATTEMPT AT A SOLUTION

My thoughts...

(A) A quick moving bee... its wings are flapping at high frequency. that would mean it has a short wavelength. But I don't think the wings is involved in the question. hehe =)

(B) electron... smaller than the wavelength of light but is still detectable. In fact, my textbook shows that its wavelength (traveling at 2% of the speed of light) is larger than a ball bearing a mass of 0.02 kg traveling at 330 m/s.

(C) elephant... my textbook says that "a particle of LARGE MASS and ordinary speed has too small a wavelength to be detected by conventional means."

(D) earth... well, it's also a large mass. But it does travel at a blazing speed.Is the answer (A) Electron?
'cuz a bee travels much slower than the electron... hmm...
Please help!
 
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  • #2
I would say electron.
p = mv

electron max v can be 3E8
bee min v can be 1

electron max is .. E-27?
bee mass is ~ E-3 or 4
 
  • #3
Why not try putting some figures in?
 
  • #4
cristo said:
Why not try putting some figures in?

Good point...

should I just make estimates? The question doesn't give any figures.
 
  • #5
rootX said:
I would say electron.
p = mv

electron max v can be 3E8
bee min v can be 1

electron max is .. E-27?
bee mass is ~ E-3 or 4
Can you translate please? hehehe :confused::smile:
I don't understand "3E8" ... "E-27"...
 
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  • #6
cristo said:
Why not try putting some figures in?

Do you think I should? It's just supposed to be a simple problem... 'What would I expect'...


But since I don't know what to expect... oh well. Fine, I'll put some figures in. :frown:
 
  • #7
1E8 = 1*10^8

don't need exact numbers
say actual bee mass is 257 g
you can use 1*10^-3 g or even 1*10^-4 g..

you should know electron mass (u will be using it a lot in physics ...)
and you must know that nothing can exceed speed of light: 3e8
 
  • #8
Ahhh... okay. E for EXPONENT. duh!

so it's 10[tex]^{8}[/tex]
 
  • #9
Well if I was faced with this question I would have to say the electron.
Why?
Well


[tex]\lambda=\frac{h}{mv}[/tex]


firstly (even though this is wrong to do) assume all move with the same velocity.
That would make [itex]\lambda \propto \frac{1}{m}[/itex]

so the one with the least mass would have the biggest wavelength...the electron has the smallest and hence the largest of them all.
 
  • #10
daNAV1GATOR said:
But since I don't know what to expect... oh well. Fine, I'll put some figures in. :frown:

Yea, just pick some numbers; it's better than just guessing! So, for an elephant, say, it has a speed of about 3m/s, mass of 1000kg, thus a momentum of 3000kgm/s. Plug this in your formula. Do the same for the other cases.
 
  • #11
Okay... the answer does seem to be (B), Electron orbiting a nucleus.

Quick moving bee = 2 x 10[tex]^{-31}[/tex] m
(0.0005 kg, 6.7 m/s)

Electron = 10[tex]^{-10}[/tex] m

Elephant = 10[tex]^{-37}[/tex] m
(3000 kg, 2 m/s)

Earth = 10[tex]^{-39}[/tex] m
(6 x 10[tex]^{24}[/tex] kg, 30,000 m/s)


T H A N K S . G U Y S ! ! !
i'M nOw dOnE wItH mY PhYsICs... pretty fun. learned a lot.
 
  • #12


ok,
we know another formula that
f=v/[tex]\lambda[/tex].
(as, [tex]\upsilon[/tex]=c/[tex]\lambda[/tex])

so,
using velocity also you can solve it.
 

1. What is the de Broglie wavelength?

The de Broglie wavelength, named after physicist Louis de Broglie, is the wavelength associated with a moving particle, such as an electron. It is a fundamental concept in quantum mechanics and is described by 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 its velocity.

2. How is the de Broglie wavelength related to the wavelength of an object?

The de Broglie wavelength is a specific type of wavelength that applies to particles, while the wavelength of an object refers to the length of a wave, such as light or sound, passing through that object. The de Broglie wavelength is used to describe the wave-like behavior of particles, while the wavelength of an object is used to describe the properties of a wave.

3. What factors affect the de Broglie wavelength?

The de Broglie wavelength is affected by the mass and velocity of the particle. As the mass increases, the wavelength decreases, and as the velocity increases, the wavelength also decreases. This is because the de Broglie wavelength is inversely proportional to the mass and velocity of the particle.

4. How is the de Broglie wavelength measured?

The de Broglie wavelength is typically measured using specialized equipment, such as an electron microscope. The wavelength can also be calculated using the aforementioned equation, if the mass and velocity of the particle are known.

5. Why is the de Broglie wavelength important in quantum mechanics?

The de Broglie wavelength is an essential concept in quantum mechanics because it helps explain the wave-particle duality of matter. This theory suggests that particles, such as electrons, exhibit both wave-like and particle-like behavior, and the de Broglie wavelength is used to describe the wave-like behavior of these particles. It also has practical applications in fields such as particle physics and nanotechnology.

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