Quantum Physics help

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).

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.

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?

Yes for both.

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.

....
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?

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?

….
(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 ….

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

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.

First of all, you really need to write the terms properly and clearly to avoid misunderstanding or wrong interpretations.


or


NOT

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

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:



The momentum of photon is NOT



because the photon has no rest mass like an electron.

The magnitude of the final momentum of the electron is just



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

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.

Can you please explain what's wrong with this conservation then? I'm probably confused with a concept.

may I please know the difference between both?

“…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:


OR


*You miss the minus sign.

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


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



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.

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.

….

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/precalculus/x9e81a4f98389efdf:vectors/x9e81a4f98389efdf:unit-vec/v/intro-unit-vector-notation

or read the following:
https://mathinsight.org/vectors_cartesian_coordinates_2d_3d