Bohr's Quantum Model: Exploring the Atom

[stickplot]

Homework Statement

In Bohr’s quantum model of the atom:

1. The energy of an electron inside the atom is an integral multiple of 13.6eV.
2. Electrons lose energy and spiral into the nucleus.
3. Gravitational forces are offset by electric forces.
4. Electrons do not radiate energy when they are in a stationary orbit
5. None of these is correct.

Homework Equations

E=-13.6 eV/n^2

The Attempt at a Solution

from the equation i would think its 1 but I am not sure because it says its an integral multiple.
and for 2 i know that if electrons lose energy they lose there negative charge and go towards the nucleus.
and for 3 i know that the electric force works like a gravitational force.
but i don't think 2 and 3 have to do with bohrs model so i think its 1 but not sure help please.

 

[Hootenanny]

You know stickplot, if you could muster up the effort to open *any* undergraduate physics text or even just Google "The Bohr Model", you would probably be given the answer.

 

[stickplot]

yes I've already seen it in wikipedia and hyperphysics, i understand the whole concept I am just not sure what the answer would be. I know bohrs model represents how negative charged electrons encircle the positive and might jump back or fourth a orbit depending on the electromagnetic energy it gains or loses.
1- i don't think its right because it says its a multiple
2- this is just a small part of bohrs model
3- it is very alike to a gravitational force but I am not sure if this explains the whole bohr model
4- not this one.

so i have been looking at this problem for a while, and I am just not sure what it would be.

 

[Hootenanny]

I agree with Stick on this Hootenany it's either they're all wrong, and terribly worded or the answer is the gravity thing, which could have been better phrased to be honest.
That doesn't preclude it from losing or emitting energy in the form of photons if it is in a stable orbit or quantisation would be a useless theory.

I disagree. According to the Bohr model, number four looks correct to me. Stable orbits were in fact the starting point for 'quantisation'

That said it's not the most well laid out question.

As I said above, I disagree. The question is perfectly well worded and answerable, if of course one knows the answer.

 

[Hootenanny]

So you are telling me that an electron in a stable orbit will not radiate energy?

According to Bohr's model, yes.

In that case how on Earth does such an electron in a stable orbit lose energy?

By emitting a photon.

What it should of said if it didn't want to be criminally misleading is something much different. Just because you think it is easy to understand is beside the point, obviously I had the same issue as the OP, I would hope that tips you off that the way the question is worded sucks, but perhaps not?

Just because two people cannot answer a question does not make that question poorly worded.

That's absolutely nothing like what it says, how you inferred that from that question is amazing.

http://theory.uwinnipeg.ca/physics/bohr/node3.html
http://www.rwc.uc.edu/koehler/biophys/6a.html

 

[cristo]

There's no point in putting up links, we know what the model says and we are well aware of how it works and why and so on,

Who is the "we" in this statement? When helping out in the homework forum, you cannot assume that the OP knows the answer to the question. Just because you don't understand the question, and a student doesn't know how to answer it, certainly does not imply that the question is badly worded.

what I and indeed the OP had a problem with is the way it was worded, it is at best unclear and at worst ambiguous.

Again, you're making assumptions left, right and centre. If you look back to the OP, you will see that the problem is not with the question, but with understanding of the model. I agree with Hootenanny that the question is quite clear, again if one knows the answer!

 

[D H]

The question blows frankly.

Hoot and cristo are correct here, Dagda. The correct answer to the question is one of the central axioms of the Bohr model.

Can you point out what is wrong with question 3, given the ambiguous use of the word offset? It's not just a single question, the whole thing is ambiguous.

Offset means cancel. Gravitation is always attractive, and so is the electrostatic interaction between a positively charged particle and negatively charged particle. How can two attractive forces offset one another?

The Bohr model doesn't talk about gravitational at all except in the sense that planets gravitationally orbiting a central star served as a motivating analogy for the model. There is one *big* problem with this analogy: from a classical perspective, an accelerating charged particle must constantly emit radiation per Maxwell's equations. Bohr's model precludes this classical radiation, and the way it does that is the key to answering this question correctly.

 

[D H]

yes I've already seen it in wikipedia and hyperphysics, i understand the whole concept I am just not sure what the answer would be. I know bohrs model represents how negative charged electrons encircle the positive and might jump back or fourth a orbit depending on the electromagnetic energy it gains or loses.

Unfortunately, the hyperphysics description of the Bohr model is rather weak, and the wiki writeup is rather long-winded.

There are four central tenets of the Bohr model:

1. Electrons orbit the nucleus in stable orbits much as planets orbit the Sun, with the Coulomb force rather than gravitation providing the centripetal force on the planetary electrons.
2. These stable electron orbits are quantized. The only permissible orbits are whose in which the angular momentum of the electron is an integral multiple of the reduced Planck constant, $\hbar = h/2\pi$.
3. Contrary to Maxwell's equations, an electron moving in one of these stable orbits does not radiate.
4. Electrons transition between stable orbits by absorbing or emitting electrmagnetic radiation.

How does this compare with the options given in the original post?

1. The energy of an electron inside the atom is an integral multiple of 13.6eV.
   Angular momentum is an integral multiple of some constant (h/2pi). Energy is not. As you already noted, energy is some constant divided by the square of an integer. So this answer is wrong.
2. Electrons lose energy and spiral into the nucleus.
   This was a problem with the Rutherford model, which preceded the Bohr model by a couple of years. Bohr's model postulates stable electron orbits. So this answer too is wrong.
3. Gravitational forces are offset by electric forces.
   The Bohr model specifically states that the Coulomb force is responsible for the stable orbits. The only place gravity comes into play at all is as a motivating analogy. Look at it this way: Gravity is a lot weaker (by a factor of 10^-39) than the Coulomb force. It simply doesn't enter into the model at all. So this is yet another incorrect answer.
4. Electrons do not radiate energy when they are in a stationary orbit.
   This is the third central tenet of the Bohr model, almost word-for-word. This is the correct answer.
5. None of these is correct.
   Since number 4 is correct, this answer is incorrect.

4- not this one.

So what made you write off the correct answer? Explain your reasoning here and we'll help steer you in the correct direction.

 

[cristo]

For example the Bohr model only talks about hydrogen in any basic physics textbook I've read, so why isn't the first one right?

Because the energy levels are not integer multiples of 13.6eV. The energy levels go like 1/n^2, which is not (in general) an integer.


This sort of comment further adds to my doubt that you are confident enough in the subject to be helping out in the homework forum.

 

[Redbelly98]

Hi stickplot,

I think you mentioned in another post that you're doing an online study, and don't own a textbook yourself. I'm going to suggest getting one, it would be helpful for looking up a lot of stuff more easily than searching online.

I like a book by Giancoli, Physics - Principles With Applications. It covers the types of questions you've been asking, and Amazon has an earlier edition for about 40 $US:

https://www.amazon.com/dp/0131021532/?tag=pfamazon01-20

For example, it talks about the Bohr model, and stationary orbits, and even says "an electron ... would move in the orbit without radiating energy".

 

[Redbelly98]

The statement Electrons do not radiate energy when they are in a stable orbit is false because of the way it is phrased, as can be shown by any experiment on any atom anywhere. Any electron in a stable orbit can emit a photon at any time, the probabilities are mapped by the Schrödinger equation.

In the Bohr model, electrons don't radiate while they remain in a stationary orbit. It allows for radiation only when jumping between different orbits.

Just to add my vote, I also thought it was obvious (if you're familiar with the model) that #4 is the answer.

1. "Integral multiple" is the same as "integer multiple"; there are no integrals (in the calculus sense) in the Bohr model.

2. The electron does not "spiral into" the nucleus. This fact was a prime motivation for needing a new theory in the first place.

3. Gravity is so weak as to not even be a consideration in the model.

With respectful regards,

Mark

 

[tiny-tim]

The questions is so ambiguous it could mean anything.
…
The statement Electrons do not radiate energy when they are in a stable orbit is false because of the way it is phrased, as can be shown by any experiment on any atom anywhere. Any electron in a stable orbit can emit a photon at any time, the probabilities are mapped by the Schrödinger equation.

Dagda, you are supposed to be helping the OP, not misleading him.

As with most exam questions, one must read the question carefully.

It says "when they are in a stationary orbit".

I fail to see how that can possibly include "when they jump from one stationary orbit to another" … which is the only time a photon could be "radiated".

Hootennany and cristo and DH are right … #4 is a clear statement of one of the principal characteristics of the Bohr model.

How is it that we must endure arrogant comments like these from a 'PF mentor' ? Especially in the 'Introductory Physics' section? Maybe a little reflection would be in order before jumping to conclusions?

This surely makes me feel like never EVER asking another question about whatsoever on this forum. So sad.

Hootenanny's advice to look at a textbook was good advice … the OP had been relying entirely on wikipedia and hyperphysics, which are not enough in some cases … the extra care taken by writers of textbooks can sometimes clarify things greatly.

Some students, through no fault of their own, are lulled into a false sense of security by the internet, and a wake-up call directing them to the world of books is sometimes helpful and appropriate.

 

[cristo]

It says integral not integer, that's my point, that could mean that the integral of wave function is a multiple of another integral, for all I know it might be, I don't know what integrals they use exactly in quantisation models. If it means integer why not say integer?

You're just trying to fight your way out of a corner you've boxed yourself into. You first say

And only in a hydrogen atom AFAIK is the value going to be an integral multiple of 13.6ev.

and now you claim not to understand what the word integral means when you used the very word in a sentence meaning integer.

This comment further reinforces my belief that you are arrogant? See both of us can play the ad hominem game? Doesn't make you right, it makes the question a pigs ear of ambiguity none the less.

Pff.. please.. I've been called a lot worse than that before, funnily enough, most of the time when people have been proven wrong about something...

 

[ZapperZ]

This thread has been locked, pending moderation. I also believe that the OP has been given sufficient answer within the context of the question and the level of the class.

Zz.