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

[daNAV1GATOR]

[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 = $$\frac{h}{momentum}$$

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!

 

[rootX]

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

 

[cristo]

Why not try putting some figures in?

 

[daNAV1GATOR]

Why not try putting some figures in?

Good point...

should I just make estimates? The question doesn't give any figures.

 

[daNAV1GATOR]

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
I don't understand "3E8" ... "E-27"...

 

[daNAV1GATOR]

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.

 

[rootX]

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

 

[daNAV1GATOR]

Ahhh... okay. E for EXPONENT. duh!

so it's 10$$^{8}$$

 

[rock.freak667]

Well if I was faced with this question I would have to say the electron.
Why?
Well


$$\lambda=\frac{h}{mv}$$


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

so the one with the least mass would have the biggest wavelength...the electron has the smallest and hence the largest of them all.

 

[cristo]

But since I don't know what to expect... oh well. Fine, I'll put some figures in.

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.

 

[daNAV1GATOR]

Okay... the answer does seem to be (B), Electron orbiting a nucleus.

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

Electron = 10$$^{-10}$$ m

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

Earth = 10$$^{-39}$$ m
(6 x 10$$^{24}$$ 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.

 

[RajChakrabrty]

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

so,
using velocity also you can solve it.