Hi! I'm confused about the concept discussed in Problem 16 of our Achieve Homework for the Quantum Unit. Can anyone help me understand this?
Problem Description:
"In 1913, Niels Bohr proposed a model of the hydrogen atom in which the electron could exist only in specific circular orbits. He did not offer any explanation as to why only those particular orbits would be allowed. In 1924, Louis de Broglie suggested that the electron could only exist in orbits corresponding to certain kinds of wave patterns.
The diagram shows an electron orbit that has been "cut and unwrapped" to better show the electron wave. Classify the wave patterns according to whether or not they are compatible with de Broglie's description of the allowed Bohr orbits of the hydrogen atom."
Achieve Homework #2, Problem 16
Moderators: Chem_Mod, Chem_Admin
-
- Posts: 50
- Joined: Fri Sep 24, 2021 6:14 am
Re: Achieve Homework #2, Problem 16
Hi!
I am also struggling with this question on Achieve, but to my understanding, to find whether or not a wave pattern is compatible or not with de Broglie's description, we need to examine whether the wave has a constant amplitude and frequency. Additionally, the wave pattern must also be a complete number of cycles, meaning that the pattern cannot be "cut" off.
I am also struggling with this question on Achieve, but to my understanding, to find whether or not a wave pattern is compatible or not with de Broglie's description, we need to examine whether the wave has a constant amplitude and frequency. Additionally, the wave pattern must also be a complete number of cycles, meaning that the pattern cannot be "cut" off.
-
- Posts: 101
- Joined: Fri Sep 24, 2021 6:13 am
Re: Achieve Homework #2, Problem 16
Just to add a bit about the "cut off" part of the question. When you look at the unwrapped version, try to imagine rejoining the ends to make a circle. If the number of cycles isn't whole, the ends won't match up.
-
- Posts: 119
- Joined: Fri Sep 24, 2021 5:34 am
Re: Achieve Homework #2, Problem 16
Hi
I was also confused with this question first. I think the main point is to understand that the wave if cut off from a circular pattern, which means when you rejoin the head and tail of the linear wave, it should still be consecutive, and this indicates that there must be an complete number of wave cycles.
I was also confused with this question first. I think the main point is to understand that the wave if cut off from a circular pattern, which means when you rejoin the head and tail of the linear wave, it should still be consecutive, and this indicates that there must be an complete number of wave cycles.
-
- Posts: 105
- Joined: Fri Sep 24, 2021 6:09 am
Re: Achieve Homework #2, Problem 16
Hello,
Basically for this question, you need to check if the wave has uniform curves (with constant amplitude), but also you need to check the ends of each wave to see if they would connect. Since the electron wave has been "cut," a compatible wave would be where the left end of one wave seamlessly connects with the right end of that wave. For example, if the left end and right end of the wave are both above the red line, they wouldn't connect to be a continuous wave. Hope this helps and please let me know if you would like me to clarify anything.
Basically for this question, you need to check if the wave has uniform curves (with constant amplitude), but also you need to check the ends of each wave to see if they would connect. Since the electron wave has been "cut," a compatible wave would be where the left end of one wave seamlessly connects with the right end of that wave. For example, if the left end and right end of the wave are both above the red line, they wouldn't connect to be a continuous wave. Hope this helps and please let me know if you would like me to clarify anything.
-
- Posts: 102
- Joined: Fri Sep 24, 2021 5:38 am
Re: Achieve Homework #2, Problem 16
Hi,
For this question, in order for the electron to exist in an orbit around the nucleus, its wave must interfere constructively with itself, similar to a standing wave on a closed loop of wire. To fit as a standing wave, each Bohr‑electron orbit must have a circumference that is equal to a whole number of complete wavelengths of the electron wave.
In short, you have to have a whole number of wavelengths (make sure there are no partial wavelengths) in order for the wave to be compatible with de Broglie's description.
For this question, in order for the electron to exist in an orbit around the nucleus, its wave must interfere constructively with itself, similar to a standing wave on a closed loop of wire. To fit as a standing wave, each Bohr‑electron orbit must have a circumference that is equal to a whole number of complete wavelengths of the electron wave.
In short, you have to have a whole number of wavelengths (make sure there are no partial wavelengths) in order for the wave to be compatible with de Broglie's description.
Return to “Properties of Light”
Who is online
Users browsing this forum: No registered users and 12 guests