Kaplan Passage Question Physics

[clemson2011]

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Hey all, so I was looking at a passage discussing the technique of Rutherford backscattering spectrometry.

The relationship between the kinetic energy (of the incident particle) and mass (of the sample atom) is a proportional relationship (increase in mass = increase in kinetic energy) according to the graph given in the passage.

The question is "For which of the following sample atoms would an alpha particle backscatter from the surface with the lowest kinematic factor?
A) Oxygen
B) nitrogen
c) carbon
d) Hydrogen

The correct answer is suppose to be Carbon, but why isnt it Hydrogen since hydrogen has the lowest mass?

 

[WhiteWashed]

Hey all, so I was looking at a passage discussing the technique of Rutherford backscattering spectrometry.

The relationship between the kinetic energy (of the incident particle) and mass (of the sample atom) is a proportional relationship (increase in mass = increase in kinetic energy) according to the graph given in the passage.

The question is "For which of the following sample atoms would an alpha particle backscatter from the surface with the lowest kinematic factor?
A) Oxygen
B) nitrogen
c) carbon
d) Hydrogen

The correct answer is suppose to be Carbon, but why isnt it Hydrogen since hydrogen has the lowest mass?

is the question assuming uniform velocity for each atom?

 

[LaurenMCAT]

Hey there clemson2011

Before I explain it in depth, think about what would happen in a collision between just about ANY particle and a hydrogen atom...

In other words, consider the mass difference! Can you even HAVE backscattering from a sample made of hydrogen atoms?

 

[clemson2011]

Hey there clemson2011

Before I explain it in depth, think about what would happen in a collision between just about ANY particle and a hydrogen atom...

In other words, consider the mass difference! Can you even HAVE backscattering from a sample made of hydrogen atoms?

So would backscattering only occur if the sample's mass was greater than the alpha particle?

Practically speaking I can picture it (Bouncy ball hitting a piece of paper, vs. bouncy ball hitting a bowling ball), you'd get backscattering in the second scenario. But does that mean if there were detectors that could detect the speed of the alpha particles that were not backscattered the graph for kinematic factor vs amu would be decreasing until the mass of the sample = the mass of the particle (where at that point it would be 0) and then begin to rise again? (A somewhat parabolic shape?)

Theoretically speaking though is it easily proven, because the only way I can begin to think about it would be the following. If momentum is conserved, therefore {M1V1i +M2V2i = M1V1f + M2V2f}. If 2 = the sample and 1 = the alpha particle, initially 2 is at rest.

Therefore M1V1i = M1V1f + M2V2f (equation 1) breaking it up into it's x and y components would yield 2 additional variables (sin(alpha) and sin(beta) )

equation 2 (Conservation of kinetic formula)
equation 3 ( trig identifies)

And then incorporate them all to find out the relationship between velocity and mass.

 

[clemson2011]

And btw thanks 🙂

 

[LaurenMCAT]

So would backscattering only occur if the sample's mass was greater than the alpha particle?

Yes! And on Test Day...you can stop there 😉 because you already are looking for a low sample atom mass and H is too small.

The equations you offered DO prove this...and, yes, that's how you could solve for rebound (backscattering) velocity and incoming particle mass.

Re: your potentially parabolic curve if you were to detect non-rebounding (or backscattered) atoms...I'm not sure if that's the actual type of slope you'd get. The problem with your hypothesis might be: if incoming atoms aren't backscattered, if they can crash through the sample, then we probably won't have elastic collisions, stuff would get deflected who knows where, and at the detector, we'd register both sample atoms and incoming atoms. 😱 Noise.