Quantum Physics help

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username5006362
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#1
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I need help with bi and c. Please explain what part c even means.
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Eimmanuel
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(Original post by UnknownCookie)
I need help with bi and c. Please explain what part c even means.
For b(i), you need to take into consideration the conservation of linear momentum in horizontal and vertical direction to draw the direction of motion of electron after "collision".

Not sure what you are asking for (c).
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(Original post by Eimmanuel)
For b(i), you need to take into consideration the conservation of linear momentum in horizontal and vertical direction to draw the direction of motion of electron after "collision".

Not sure what you are asking for (c).
For bi I'll try solving it as how I think it is:

Initial horizontal momentum = final horizontal momentum

0 + x = x

Vertical initial momentum = final vertical momentum

0 + 0 = x + (-x)

Since the electron has negative vertical momentum after the collision as deduced above, it must be moving diagonally towards bottom right.


And for (c), determining only magnitude of momentum means we simply multiply the mass with resultant velocity instead of considering calculation of momentum separately for horizontal and vertical direction?
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Eimmanuel
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(Original post by UnknownCookie)
For bi I'll try solving it as how I think it is:

Initial horizontal momentum = final horizontal momentum

0 + x = x

Vertical initial momentum = final vertical momentum

0 + 0 = x + (-x)

Since the electron has negative vertical momentum after the collision as deduced above, it must be moving diagonally towards bottom right.


And for (c), determining only magnitude of momentum means we simply multiply the mass with resultant velocity instead of considering calculation of momentum separately for horizontal and vertical direction?
Yes for both.
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(Original post by Eimmanuel)
Yes for both.
Ok, so according to (c) the linear momentum should have been conserved as:

Initial momentum before collision = final momentum after collision

(v is initial resultant velocity and hence m×v is initial resultant momentum of photon) m × v + 0 ( initial momentum of electron) = m × v1 (where v1 is resultant velocity of photon after collision and hence mv1 is final resultant momentum of photon ) + x ( final resultant momentum of the electron is denoted by x)

But this is obviously wrong because we need to consider conservation according to the direction as done above.

I hope my understanding of part (c) correct?
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Eimmanuel
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(Original post by UnknownCookie)
Ok, so according to (c) the linear momentum should have been conserved as:

Initial momentum before collision = final momentum after collision

(v is initial resultant velocity and hence m×v is initial resultant momentum of photon) m × v + 0 ( initial momentum of electron) = m × v1 (where v1 is resultant velocity of photon after collision and hence mv1 is final resultant momentum of photon ) + x ( final resultant momentum of the electron is denoted by x)

But this is obviously wrong because we need to consider conservation according to the direction as done above.

I hope my understanding of part (c) correct?
(Original post by Eimmanuel)
Yes for both.
Maybe I have confused you with my reply.

v is initial resultant velocity and hence m×v is initial resultant momentum of photon) m × v + 0 ( initial momentum of electron) = m × v1 (where v1 is resultant velocity of photon after collision and hence mv1 is final resultant momentum of photon ) + x ( final resultant momentum of the electron is denoted by x)
B....we need to consider conservation according to the direction as done above.
Both are conservation of linear momentum.

(Original post by UnknownCookie)
....
And for (c), determining only magnitude of momentum means we simply multiply the mass with resultant velocity instead of considering calculation of momentum separately for horizontal and vertical direction?
This is confusing. Magnitude of momentum has no direction and when I say yes to this what I thought you mean that "magnitude of momentum means mass with magnitude of resultant velocity".
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username5006362
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(Original post by Eimmanuel)
Maybe I have confused you with my reply.





Both are conservation of linear momentum.



This is confusing. Magnitude of momentum has no direction and when I say yes to this what I thought you mean that "magnitude of momentum means mass with magnitude of resultant velocity".
Magnitude of momentum = mass × speed/resultant velocity.
The velocity here isn't horizontal or vertical velocity I believe. But just the resultant velocity of the horizontal and vertical velocity.


And when we consider conservation of magnitude of linear momentum doesn't it mean we are simply using the resultant velocity of the bodies moving at an angle and hence creating just one equation, instead of solving for horizontal and vertical directions separately using 2 equations (as shown in one of the replies above)?

Can you please explain where I'm wrong?
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Eimmanuel
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(Original post by UnknownCookie)
Magnitude of momentum = mass × speed/resultant velocity.
The velocity here isn't horizontal or vertical velocity I believe. But just the resultant velocity of the horizontal and vertical velocity.

And when we consider conservation of magnitude of linear momentum doesn't it mean we are simply using the resultant velocity of the bodies moving at an angle and hence creating just one equation, instead of solving for horizontal and vertical directions separately using 2 equations (as shown in one of the replies above)?

Can you please explain where I'm wrong?
First of all, you really need to write the terms properly and clearly to avoid misunderstanding or wrong interpretations.


magnitude of linear momentum = mass × speed
or

magnitude of linear momentum = mass × magnitude of the resultant velocity

NOT

magnitude of linear momentum = mass × resultant velocitymagnitude of linear momentum = mass × velocity


Linear momentum, velocity and resultant velocity are vector quantities while magnitude implies positive scalar.

There is no conservation of magnitude of linear momentum in physics ONLY conservation of linear momentum.



(Original post by UnknownCookie)
….
(v is initial resultant velocity and hence m×v is initial resultant momentum of photon) m × v + 0 ( initial momentum of electron) = m × v1 (where v1 is resultant velocity of photon after collision and hence mv1 is final resultant momentum of photon ) + x ( final resultant momentum of the electron is denoted by x)

But this is obviously wrong ….
I am not sure why this is not conservation of linear momentum. I would consider this is conservation of linear momentum in a vector form if I ignore some of the wrong descriptions.

We can write the conservation of linear momentum in vector form:


 \vec{p}_{\text{photon, initial}} = \vec{p}_{\text{electron, final}} + \vec{p}_{\text{photon, final}}

The momentum of photon is NOT


momentum of photon = mass of photon × velocity of photon

because the photon has no rest mass like an electron.

(Original post by UnknownCookie)
….But this is obviously wrong because we need to consider conservation according to the direction as done above.
We can also consider conservation of linear momentum in component form:


 {p}_{x, \text{photon, initial}} = {p}_{x, \text{electron, final}} + {p}_{x,\text{photon, final}}


 {p}_{y, \text{photon, initial}} = {p}_{y, \text{electron, final}} + {p}_{y,\text{photon, final}}

How you want to deal with conservation of linear momentum is your own choice of preference.

Explain why the magnitude of the final momentum of the electron is not equal to the change in magnitude of the momentum of the photon.
The magnitude of the final momentum of the electron is just


mass of electron × speed of electron after “collision”

while the change in magnitude of the momentum of the photon is just


|magnitude of final momentum of photon – magnitude of initial momentum of photon|
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(Original post by Eimmanuel)
First of all, you really need to write the terms properly and clearly to avoid misunderstanding or wrong interpretations.


magnitude of linear momentum = mass × speed
or

magnitude of linear momentum = mass × magnitude of the resultant velocity

NOT

magnitude of linear momentum = mass × resultant velocitymagnitude of linear momentum = mass × velocity
I'm really sorry. I admit I made things quite messy there.



(Original post by Eimmanuel)
There is no conservation of magnitude of linear momentum in physics ONLY conservation of linear momentum.
may I please know the difference between both?





(Original post by Eimmanuel)
I am not sure why this is not conservation of linear momentum. I would consider this is conservation of linear momentum in a vector form if I ignore some of the wrong descriptions.

We can write the conservation of linear momentum in vector form:


 \vec{p}_{\text{photon, initial}} = \vec{p}_{\text{electron, final}} + \vec{p}_{\text{photon, final}}

The momentum of photon is NOT


momentum of photon = mass of photon × velocity of photon

because the photon has no rest mass like an electron.
Oh, sorry! I had forgotten that's not how you determine the momentum of a photon.

I honestly didn't even know before you can consider conservation of linear momentum by equating the resultant momentum of both the bodies before and after collision! Always thought only the x components of the two bodies before the collision are equal to the x components after collision, y components of the two bodies before the collision are equal to y components after collision, and that the resultant momentum for the 2 bodies before and after collision isn't conserved. Explains part of my confusion I guess.





(Original post by Eimmanuel)
The magnitude of the final momentum of the electron is just


mass of electron × speed of electron after “collision”

while the change in magnitude of the momentum of the photon is just


|magnitude of final momentum of photon – magnitude of initial momentum of photon|
initial momentum of photon + 0 = final momentum of photon + final momentum of electron

This is conservation of momentum not in component form, but conservation of resultant momentum for the bodies. We can calculate the final momentum of electron and it really comes out to be equal to the change in momentum of the photon just as the question says it cant be, but from this conservation it is just that. Can you please explain what's wrong with this conservation then? I'm probably confused with a concept.


P.S: resultant momentum = the resultant component of the x and y components of momentum.
Added this detail because I probably may be using the wrong term.
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Eimmanuel
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(Original post by UnknownCookie)
I'm really sorry. I admit I made things quite messy there.

may I please know the difference between both?

Oh, sorry! I had forgotten that's not how you determine the momentum of a photon.

I honestly didn't even know before you can consider conservation of linear momentum by equating the resultant momentum of both the bodies before and after collision! Always thought only the x components of the two bodies before the collision are equal to the x components after collision, y components of the two bodies before the collision are equal to y components after collision, and that the resultant momentum for the 2 bodies before and after collision isn't conserved. Explains part of my confusion I guess.

initial momentum of photon + 0 = final momentum of photon + final momentum of electron

This is conservation of momentum not in component form, but conservation of resultant momentum for the bodies. We can calculate the final momentum of electron and it really comes out to be equal to the change in momentum of the photon just as the question says it cant be, but from this conservation it is just that. Can you please explain what's wrong with this conservation then? I'm probably confused with a concept.

P.S: resultant momentum = the resultant component of the x and y components of momentum.
Added this detail because I probably may be using the wrong term.
We can calculate the final momentum of electron and it really comes out to be equal to the change in momentum of the photon just as the question says it cant be, but from this conservation it is just that.
“…calculate the final momentum of electron and it really comes out to be equal to the change in momentum of the photon…” this is conservation of linear momentum (except something is missing see below*) NOT what the question said that they cannot be equal. The question said another thing.


Can you please explain what's wrong with this conservation then? I'm probably confused with a concept.
Both questions are actually the same. It is best illustrated with an example.

Consider a particle of mass m1 with only horizontal momentum say 5 N⋅s i collides obliquely with another particle of mass m2 at rest.

After collision, m1 has the linear momentum of (3 N⋅s i + 2 N⋅s j) and m2 has the linear momentum of (2 N⋅s i ‒ 2 N⋅s j).

Note that i and j are the unit vector along x and y direction, respectively.

Conservation of linear momentum:


total initial linear momentum = total final linear momentum
5 N⋅s i + 0 = (3 N⋅s i + 2 N⋅s j) + (2 N⋅s i ‒ 2 N⋅s j)
OR

Change in linear momentum of m1 = ‒ Change in linear momentum of m2
(3 N⋅s i + 2 N⋅s j) ‒ 5 N⋅s i = ‒ (2 N⋅s i ‒ 2 N⋅s j)

*You miss the minus sign.

The change in magnitude of the linear momentum of the m1 is

|magnitude of final linear momentum of m1 – magnitude of initial linear momentum of m1|


 | (\sqrt{3^2 + 2^2} - \sqrt{5^2} | = 1.394 )

The change in magnitude of the linear momentum of the m2 is

 | \sqrt{2^2 + 2^2}| = 2.828 )


Obviously,
Change in the magnitude of the linear momentum of m1 is NOT equal to change in magnitude of the linear momentum of m2.

There is also one thing which students tend to misunderstand:
Change in the magnitude of the linear momentum of m1 is NOT equal to the magnitude of change in the linear momentum of m1.

I am not sure are you one of those.

Spoiler:
Show


I have already computed the change in the linear momentum of m1 above.

magnitude of change in the linear momentum of m1 is

 | \sqrt{(-2)^2 + 2^2}| = 2.828 )


may I please know the difference between both?
When I say there is no conservation of magnitude of linear momentum in physics is because (as fas I know) physicists do not use such ambiguous phrase and I also do not understand what do you mean by the conservation of magnitude of linear momentum. Can you show me a reference (a physics text is written by physicists NOT A level physics text or a published paper) that use conservation of magnitude of linear momentum?

You really need to pay attention to the way how people write physics terms and do not add your own interpretations. A lot of students’ confusions is self-confusion where they self-introduce confusing terms to confuse themselves and then blame the teacher for not explaining concepts clearly.
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username5006362
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(Original post by Eimmanuel)
“…calculate the final momentum of electron and it really comes out to be equal to the change in momentum of the photon…” this is conservation of linear momentum (except something is missing see below*) NOT what the question said that they cannot be equal. The question said another thing.




Both questions are actually the same. It is best illustrated with an example.

Consider a particle of mass m1 with only horizontal momentum say 5 N⋅s i collides obliquely with another particle of mass m2 at rest.

After collision, m1 has the linear momentum of (3 N⋅s i + 2 N⋅s j) and m2 has the linear momentum of (2 N⋅s i ‒ 2 N⋅s j).

Note that i and j are the unit vector along x and y direction, respectively.

Conservation of linear momentum:

total initial linear momentum = total final linear momentum5 N⋅s i + 0 = (3 N⋅s i + 2 N⋅s j) + (2 N⋅s i ‒ 2 N⋅s j)
OR
Change in linear momentum of m1 = ‒ Change in linear momentum of m2 (3 N⋅s i + 2 N⋅s j) ‒ 5 N⋅s i = ‒ (2 N⋅s i ‒ 2 N⋅s j)

*You miss the minus sign.

The change in magnitude of the linear momentum of the m1 is
|magnitude of final linear momentum of m1 – magnitude of initial linear momentum of m1|

 | (\sqrt{3^2 + 2^2} - \sqrt{5^2} | = 1.394 )

The change in magnitude of the linear momentum of the m2 is
 | \sqrt{2^2 + 2^2}| = 2.828 )


Obviously,
Change in the magnitude of the linear momentum of m1 is NOT equal to change in magnitude of the linear momentum of m2.
I now understand that the change in magnitude of linear momentum isn't same for 2 bodies, but it's the change in momentum in vector form which is conserved in a collision and not the magnitude of the change in momentum.

However, I still have a question. What's a unit vector? Not sure what those letters with the value of momentum denote.

(Original post by Eimmanuel)
There is also one thing which students tend to misunderstand:
Change in the magnitude of the linear momentum of m1 is NOT equal to the magnitude of change in the linear momentum of m1.

I am not sure are you one of those.
I reread what you wrote several times and then managed to understand what it means.



(Original post by Eimmanuel)
When I say there is no conservation of magnitude of linear momentum in physics is because (as fas I know) physicists do not use such ambiguous phrase and I also do not understand what do you mean by the conservation of magnitude of linear momentum. Can you show me a reference (a physics text is written by physicists NOT A level physics text or a published paper) that use conservation of magnitude of linear momentum?

You really need to pay attention to the way how people write physics terms and do not add your own interpretations. A lot of students’ confusions is self-confusion where they self-introduce confusing terms to confuse themselves and then blame the teacher for not explaining concepts clearly.
I understand.
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Eimmanuel
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(Original post by UnknownCookie)
….

However, I still have a question. What's a unit vector? Not sure what those letters with the value of momentum denote.
You surprised me if you have not heard what is a unit vector at A level.
Watch the video below.
https://www.khanacademy.org/math/pre...ector-notation

or read the following:
https://mathinsight.org/vectors_cart...rdinates_2d_3d
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username5006362
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(Original post by Eimmanuel)
You surprised me if you have not heard what is a unit vector at A level.
Watch the video below.
https://www.khanacademy.org/math/pre...ector-notation

or read the following:
https://mathinsight.org/vectors_cart...rdinates_2d_3d
I understand now. Thanks for the help!
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