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CasedIt
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#1
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trying to attempt some past paper questions

A simple model of a crystal assumes that the atms in it are vibrating in the same way as a mass in a mass-spring system such as that shown in the diagram. The inter-atomic bonds behave like springs and have a 'spring constant' k.

In one instance an atom in a crystal lattice vibrates with SHM of frequency 1.0 x 10^13 Hz. The energy of an atom at room temp is approx: 4.2 x 10^-21 J

A) calculate the max. velocity of an atom of mass 3.7 x 10 - 26 kg when trapped in a crystal lattice at room temp

B) Determine the amplitude of the oscillation of the atom

C) Determine the 'spring constant' k of the inter-atomic bonds holding the attom in the lattics

D) when radiation of different frequencies falls on the crystal, one frequency is absorbed because it causes sharp resonance

explain what is meant by resonance

E) Explain why atoms are likely to have a shap resonance whereas resonance of a mass-spring system set up in the lab is likely to be sharp
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elpaw
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Is the mass of the atom given?
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DazzYaa7
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hi let me get a pen, paper and my sexy calculator...

k
:P

ok a)

id use the Kinetic energy eq

Ek = 1/2 mv^2

4.2 x 10 - 21 = 1/2 x 3.7 x 10^-26 x v2

vMAX = square root of 227027 = 476.5 ms^-1

b) Vmax = wA therefore A = Vmax/W W IS THE SAME AS 2PIF!!!!
therefore it can be vmax/2piF

476.5/2 x pi x 1 x 10^13 = 7.58 x 10-12 m

c) spring constant... 1/2 KA ^- 2 = 1/2 mw^2 A^2

therfore K = mw^2 ....

**** it

D) resonance is when a driving force that is applied to an oscillating system at the same frequency as the natural frequency of the system and the amplitude of oscillation becomes much larger

E) a larger mass would experience a frictional force as atoms do not.... forces that experience friction cause damped oscillations and reduce the sharpness of the resonance
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DazzYaa7
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(Original post by elpaw)
Is the mass of the atom given?
yeah read the question
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DazzYaa7
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(Original post by elpaw)
Is the mass of the atom given?
do C for him , it threw up me off kthx.
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Golden Maverick
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(Original post by CasedIt)
trying to attempt some past paper questions

A simple model of a crystal assumes that the atms in it are vibrating in the same way as a mass in a mass-spring system such as that shown in the diagram. The inter-atomic bonds behave like springs and have a 'spring constant' k.

In one instance an atom in a crystal lattice vibrates with SHM of frequency 1.0 x 10^13 Hz. The energy of an atom at room temp is approx: 4.2 x 10^-21 J

A) calculate the max. velocity of an atom of mass 3.7 x 10 - 26 kg when trapped in a crystal lattice at room temp
KE = 0.5 m v^2
Root((2* 4.2 x 10^-21 ) / ( 3.7 x 10 - 26 ))
= 476 m/s (to 3 s.f)
Edit: too late!
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elpaw
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(Original post by DazzYaa7)
yeah read the question
duh!


c)

W = root(k/m) => k = w²m = 3.7e-26 * (2 pi * 1e13)² = 146 N/m
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DazzYaa7
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(Original post by elpaw)
duh!


c)

W = root(k/m) => k = w²m = 3.7e-26 * (2 pi * 1e13)² = 146 N/m
i jst worked it out and got that

did 1/2 kA^2 = 1/2 mw^2 A^2

which is therefore K = mw2 which = 146 ====>>>KGS^-2 <====
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elpaw
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(Original post by DazzYaa7)
====>>>KGS^-2 <====
N/m and Kg/s² are equivalent.
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CasedIt
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thank you so much

DazzYa thank you
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DazzYaa7
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#11
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(Original post by CasedIt)
thank you so much

DazzYa thank you
you're welcome friend - i wish you luck in your forthcoming exams.

remember we are a team
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Bilal
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#12
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Hey daz speaking to yourself again?
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idiopathic
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#13
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(Original post by Bilal786)
Hey daz speaking to yourself again?
????
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Bilal
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(Original post by endeavour)
????
It was daz who replied to himself here: 'CasedIt' and 'Dazzzyyya77' are both him. He's a sad case.
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