Problem 1.
Broglie's hypothesis that prticles of momentum p with wavelength=h/p,
an 80kg student has grown concerned about being diffracted when
passing through a 75-cm wide doorway.Assuming that significant
diffraction occurs when the width of diffraction aperture is less that
10 times the wavelength of the wave being diffracted. a) determine the
max. speed at which student can pass through the doorway in order to
be significantly diffracted.b) with that speed how long with it take
the student to pass through the door way if it is 15 cm thick. c) by
comparing the result with current age of univers (4x^17) should the
student worry about being diffracted?
I need this by tomorrow morning no later than 10 AM (8/7/02)  thanks

---

Request for Question Clarification by blader-ga on 06 Aug 2002 17:34 PDT

Dear guga:

It's against Google Answer's policies to directly solve homework
problems for you. We can, however, point you to resources that explain
the methods and concepts behind the problem.

Best Regards,
blader-ga

---

Clarification of Question by guga-ga on 08 Aug 2002 04:10 PDT

I think that you are right  so get and post it prblem. 
thank you

OK! I'm glad I was able to be helpful; it's certainly an interesting
question. There are some amazingly beautiful and interesting things
out there in physics actually!

OK:

Suppose a particle mass of m kg is moving in a straight line and no 
acceleration with velocity v m/sec much smaller than the speed of 
light (so we neglect relativistic effects). I will also neglect any 
possible external electrical fields or other forces. 
 
The de Broglie hypothesis states that this particle can display wave 
properties of a wave of wavelength lambda=h/p where: 
 
 h = 6.63 * 10^(-34) joules/second (Plank's constant) 
 
 p = m * v meters meters/second 
 
 lambda = h/p meters 
 
Let's say that w is the width of our doorway. 
 
Whenever w<10*lambda we have diffraction occurring, according to the 
problem statement. 
 
 diffraction occurs  
 
     iff 
 
 w<10 * lambda  
 
 
    iff 
 
 w < 10 * h / p 
 
    iff 
 
 p < 10 * h /w [since we assume p and w are both >0] 
 
   iff 
 
 m * v < 10 * h / w 
 
   iff 
 
 v < 10 * h/(w * m) 
 
Hence, the maximum speed at which diffraction occurs is: 
 
 v=10*h/(w*m) meters/second 
 
Now if we assume the student is a particle, and thus has no width or
depth, then
the time for the student to pass through the doorway of thickness H is
 
 velocity = distance / time , so 
 
 time = distance / velocity  
 
 so  
 
 t = H/v . 
 
When you plug in the numbers here, you just have to make sure to
change the doorway length units to meters from centimeters.
 
So: w=.75 
    h=6.63*10^(-34) 
    m=80 
    H=.15 
    v=10*h/(w*m) = 10 * 6.63*10^(-34) / (.75 * 80) 
    v=1.11 times 10^{-34} meters per second . 
    t=H/v = .15 / 1.11 = 1.35 * 10^{33} seconds 
 
So (a) and (b) have answers of respectively 1.11 times 10^(-34) meters
per second and 1.35*10^{33} seconds. 
 
I don't quite understand part (c). What does the age of the universe 
have to do with whether the student should be concerned or not? 
Certainly the answer in b is much longer than the age of the universe,
but this isn't relevant to the question "should the student worry 
about being diffracted". 
 
Suppose hypothetically the same question were asked in 10^100 years
(that's
a *google* years of course). 
 
Then the age of the universe would be much longer than the time 
required to pass through the doorway, so is the implication that the 
student should *not* be concerned?  
 
Basically, I fail to see how the question of the age of the universe 
is relevant to the question of whether the student is concerned by the
time required to pass through the doorway. The student might be 
concerned by the length of the future of the universe (he wouldn't 
want to take longer than that), or the future of himself, or even of 
reaching his class on time. But the past age of the universe is not in
any way relevant that I can see. 
 
I will say that I personally would not be concerned by an effect that
only arose when I passed a doorway for a longer time period than a 
million or two years, much less billions and billions of years. I 
might be more concerned by being a widthless, depthless particle than
being diffracted in the first case, though I wouldn't mind weighing 
just 65kg again.

---

Clarification of Answer by rbnn-ga on 08 Aug 2002 10:46 PDT

Hi there,

I just wanted to add two quick comments here:

First, I should point explicitly exactly why I changed centimeters to
meters in the door width, and why, once I did that, I could ignore
units basically. The reason is that all the constants like h in
physics are given normally in what's called the International System
of Units (SI) for which length is meters, mass is kilograms, and time
is seconds (see http://physics.nist.gov/cuu/Units/units.html )

Second, I want to add what I always add to my answers: if you have any
questions or would like additional detail on any part of my solution,
please don't hesitate to ask; I'll do my best to clarify what I can.

Regards,
rbnn-ga

Sorry, I don't know enough physics to help, although it looks like an
interesting question.

 De Broglie's hypothesis concerns single particles, but the student is
ipso facto not a particle, but a system of particles. An idea of the
complexity involved in treating systems of particles under De
Broglie's hypothesis is at:
http://www.icad.org/websiteV2.0/Conferences/ICAD2000/PDFs/BobSturmICAD.pdf

Probably the intention is to treat the student as a particle? However,
if so, can the student really be concerned or worried about things? If
the student has the complexity to have emotions, he cannot be a
particle, so I'm not certain that the de Broglie hypothesis applies.

That is, had the problem just stated, "a 50 kg particle passes through
a door with speed v" I think one could apply De Broglie's hypothesis,
but that is not the problem statement.

I am certainly curious about the answer though. I know that sometimes
we can treat systems of particles as being one particle, typically in
dynamics calculations when we can treat a system of particles, in many
cases, as a single particle located at the center of mass of the
system, but I don't know one way or the other how this works vis-a-vis
de Broglie.

Suppose a particle mass of m kg is moving in a straight line and no
acceleration with velocity v m/sec much smaller than the speed of
light (so we neglect relativistic effects). I will also neglect any
possible external electrical fields or other forces.

The de Broglie hypothesis states that this particle can display wave
properties of a wave of wavelength lambda=h/p where:

 h = 6.63 * 10^(-34) joules/second (Plank's constant)

 p = m * v meters meters/second

 lambda = h/p meters

Let's say that w is the width of our doorway.

Whenever w<10*lambda we have diffraction occurring, according to the
problem statement.

 diffraction occurs 

     iff

 w<10 * lambda 


    iff

 w < 10 * h / p

    iff

 p < 10 * h /w [since we assume p and w are both >0]

   iff

 m * v < 10 * h / w

   iff

 v < 10 * h/(w * m)

Hence, the maximum speed at which diffraction occurs is:

 v=10*h/(w*m) meters/second

Now if we assume the student is a particle, and thus has no width or
depth, then
the time for the student to pass through the doorway of thickness H is

 velocity = distance / time , so

 time = distance / velocity 

 so 

 t = H/v .

When you plug in the numbers here, you just have to make sure to
change the doorway length units to meters from centimeters.

So: w=.75
    h=6.63*10^(-34)
    m=80
    H=.15
    v=10*h/(w*m) = 10 * 6.63*10^(-34) / (.75 * 80)
    v=1.11 times 10^{-34} meters per second .
    t=H/v = .15 / 1.11 = 1.35 * 10^{33} seconds

So (a) and (b) have answers of respectively 1.11 times 10^(-34) meters
per second and 1.35*10^{33} seconds.

I don't quite understand part (c). What does the age of the universe
have to do with whether the student should be concerned or not?
Certainly the answer in b is much longer than the age of the universe,
but this isn't relevant to the question "should the student worry
about being diffracted".

Suppose hypothetically the same question were asked in 10^100 (that's
a *google* years of course).

Then the age of the universe would be much longer than the time
required to pass through the doorway, so is the implication that the
student should *not* be concerned? 

Basically, I fail to see how the question of the age of the universe
is relevant to the question of whether the student is concerned by the
time required to pass through the doorway. The student might be
concerned by the length of the future of the universe (he wouldn't
want to take longer than that), or the future of himself, or even of
reaching his class on time. But the past age of the universe is not in
any way relevant that I can see.

I will say that I personally would not be concerned by an effect that
only arose when I passed a doorway for a longer time period than a
million or two years, much less billions and billions of years. I
might be more concerned by being a widthless, depthless particle than
being diffracted in the first case, though I wouldn't mind weighing
just 65kg again.

Well I hope this helps you! I'm posting this as a comment not as an
answer, since I don't really know much beyond first-year physics, and
I did make some simplifications. I realize thought that you are in a
great rush, so I am doing my best; maybe someone with more expertise
can help out.

But if this answer suits your needs I'd be happy to repost it as an
answer and collect the reward!