Oxford PAT 2016

http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_Paper3_2005_QP.pdf
Question 2 Part (c) i don't get how the pressure is related to L. I can derive something in terms of x but it doesn't seem right
Question 3 part b(iii) am i just supposed to replace Mp by Mp+Mass of neutron ?
Part (c) ii) beats me
Question 4 b) ii) i'm not exactly sure about how to relate y to the intensity. I tried considering a small thickness delta y but it gets complex really fast
EDIT: I think i was just being dumb on 4 b) ii), I think i should just be able to consider a differential element dx and use 4 a) to solve the differential equation i get and 4b) i) for the limits of the differential equation. I'm assuming that the question wants me to find the intensity only at a height y and not the intensity from 0 to y.

If anyone looks at this and gets scared of pat for some reason : This is way harder than the Pat don't worry

Does anyone know a website that explains electron spin at a higher level and in a comprehensible way?

Does anyone know a website that explains electron spin at a higher level and in a comprehensible way?

Are you looking for an explanation based on Schrodinger's equation?

Part c (ii) You should have found out K.E = h^2/(2m lambda^2) in part one. Then equating kq^2/r^2 (for hydrogen, or equivalent if you are doing for some other atoms) to mv^2/r and then writing 2 K.E for mv^2 should give you h^2/(m lambda^2) = kq^2/r with very little algebra.

Now for modelling a discrete energy system, you could set that r can only take certain values (n times something with dimension of length where n is positive integer) and nothing between. Then find energy level for corresponding values of n. Hurray!!

If you have studied Bohr's model of atom, at some point he says that r can take only those values such that angular momentum (mvr) of electrons is an integer multiple of nh/2pi.


Hope this helps.

I got T = 2pi sqrt( mp X me / k(mp + me)) and f = 1/T. So, you could replace mp by (mp + mn).

We got the same thing gr8!
How did you get this answer though ( my method seemed a bit sneaky, i basically got two expressions for the acceleration of each mass, then i used some sort of subsitution to solve it, is there a more general way to solve this ?)

Yep i got to the
h^2/(m lambda^2) = kq^2/r part but i couldnt figure out how to use this to show discrete values.
I didnt study that xD i looked up angular momentum and i got it now thanks but would you happen to know why it should be an integer multiple of nh/2pi ? the only thing i could find is something about standing waves
Is it something like quantisation of charge but in this case its quantisation of angular momentum ?
EDIT: Ok i got it : Basically the wave of the electron will interfere with itself and thus if we need it exist we need constructive interference. so 2pi*r=nlambda and from there we can show discrete energy levels with some algebra. ( i think xD) another way to think of this is, if the wave of the electron does not produce a standing wave, then it implies the position of the wave moves and the electron moves, but in the paragraph we are told that accelerating charged particles release energy ( and this is a problem ) so the only way a wave would work was if it was a standing wave. I think im all cleared now
Thanks

I did a little bit of cheating . I can find by first principle (which I didn't do in order to save time), T=2pi sqrt (m/k).

Firstly, I assumed stationary point to be at distance x from proton. Then two lengths are x and (l-x) respectively. Then I found corresponding value of k for each. (For given material of constant cross - sectional area k is inversely proportional to length). Using this information I found k for corresponding bits to be kl/x and kl/(x-l) respectively. I then plugged in those ks in equation for time for both proton and electron and equated to find x = {me/(mp + me)}l. Then using that value of x in kl/x I found required answer.

We got the same thing gr8!
How did you get this answer though ( my method seemed a bit sneaky, i basically got two expressions for the acceleration of each mass, then i used some sort of subsitution to solve it, is there a more general way to solve this ?)

How are you guys doing these kind of questions?! I literally have no idea what that is

How are you guys doing these kind of questions?! I literally have no idea what that is

Same what topic even is it xD

I happened to solve this question by chance. I can't solve almost 80% of the question in that paper. Anyway you solve these kinds of problems in M3 (springs/ SHM or something equivalent)

So we shouldn't worry about that for the PAT?

Obviously, you shouldn't worry about the question

Not to scare you but the following two concepts are frequently required in PAT.

Spring constant k, is inversely proportional to length and T = 2pi sqrt (m/k).

What is the T = 2pi sqrt (m/k) formula for and what section of an a2 physics book can i find it in?

What is the T = 2pi sqrt (m/k) formula for and what section of an a2 physics book can i find it in?

Look up simple harmonic motion

You can find that in Oscillations/ SHM section and mass-spring system sub-section of your physics book. It is to find out time period of oscillations of mass attached to spring.

I did a little bit of cheating . I can find by first principle (which I didn't do in order to save time), T=2pi sqrt (m/k).

Firstly, I assumed stationary point to be at distance x from proton. Then two lengths are x and (l-x) respectively. Then I found corresponding value of k for each. (For given material of constant cross - sectional area k is inversely proportional to length). Using this information I found k for corresponding bits to be kl/x and kl/(x-l) respectively. I then plugged in those ks in equation for time for both proton and electron and equated to find x = {me/(mp + me)}l. Then using that value of x in kl/x I found required answer.

edit: Finding acceleration and using Newton's laws is the standard way of doing this by using first principle. So, I think your method should be more general way of solving this.

Hey guys what is the reference letter supposed to have in it? My teacher said I can give her points to focus on