• Support PF! Buy your school textbooks, materials and every day products Here!

De Broglie wavelength question.

  • Thread starter physecks
  • Start date
  • #1
5
0

Homework Statement



Earth has the mass 6 · 10^24 kg and the orbit radius r = 1.5 · 10^11 m.
(a) Compute its de Broglie wavelength. (b) Apply de Broglie quantization condition
as in the case of the Hydrogen atom and compute the quantum number n for the
orbit of Earth. (c) What is the difference between the radius of nth and n + 1th
orbit?

Homework Equations



lamba=h/p=h/mv

The Attempt at a Solution



I am using the above equation to solve this but im stuck at getting the velocity of earth. I am completely stumped.
 

Answers and Replies

  • #2
674
2
Well you know lambda will need to be periodic about the circumference of a circle. So what would you get for lambda if the radius of the circle is 'r'?
 
  • #3
5
0
I'm not sure I follow what you are asking.
 
  • #4
674
2
If you drew a wave around the circumference of a circle, you will need to connect the wave back to itself. Otherwise you will have a discontinuity when try reattaching the wave back on itself. So the wave will need to be periodic around the circle, so it is continuous the whole way around.
 
  • #5
5
0
Yes, but I don't understand the relationship between the wavelength and the radius.
 
  • #6
674
2
Well if you straightened out the circumference of the circle into a box of length L. Then you specify that the wave at both ends of the box need to be periodic, you are left with the only possibilities of:

[tex]L = n\lambda[/tex]

where n=1,2,3... Now going back to the circle, ask yourself what is L for a circle?
 
  • #7
5
0
Yea L is the circumference of the circle. I understand I use the equation n*lambda=2*pi*r for b. I am stuck at a) because I am not given the velocity for earth and asked to figure out the de Broglie.
 
  • #8
674
2
Well you will have to compute the velocity the old fashioned way. You know the period of the orbit of the earth. It is just 1 year. Using that and the radius, get a speed.
 
  • #9
5
0
oh wow. Thank you so much!
 

Related Threads on De Broglie wavelength question.

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
970
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
3
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
13
Views
5K
  • Last Post
Replies
1
Views
10K
Top