# De Broglie wavelength question.

## 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?

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.

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'?

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.

Yes, but I don't understand the relationship between the wavelength and the radius.

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:

$$L = n\lambda$$

where n=1,2,3... Now going back to the circle, ask yourself what is L for a circle?

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.

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.

oh wow. Thank you so much!