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

  • #1
[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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Answers and Replies

  • #2
378
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
cristo
Staff Emeritus
Science Advisor
8,107
72
Why not try putting some figures in?
 
  • #4
Why not try putting some figures in?
Good point...

should I just make estimates? The question doesn't give any figures.
 
  • #5
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
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
378
2
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
rock.freak667
Homework Helper
6,230
31
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
cristo
Staff Emeritus
Science Advisor
8,107
72
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.
 

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