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Physics - sum1 help

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
Reply 1
Avatar for elpaw
elpaw
15
Is the mass of the atom given?
Reply 2
Avatar for DazzYaa7
DazzYaa7
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 ....

fuck 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
Reply 3
Avatar for DazzYaa7
DazzYaa7
elpaw
Is the mass of the atom given?


yeah read the question
Reply 4
Avatar for DazzYaa7
DazzYaa7
elpaw
Is the mass of the atom given?


do C for him , it threw up me off kthx.
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!
Reply 6
Avatar for elpaw
elpaw
15
DazzYaa7
yeah read the question

duh! :redface:


c)

W = root(k/m) => k = w²m = 3.7e-26 * (2 pi * 1e13)² = 146 N/m
Reply 7
Avatar for DazzYaa7
DazzYaa7
elpaw
duh! :redface:


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 <====
Reply 8
Avatar for elpaw
elpaw
15
DazzYaa7
====>>>KGS^-2 <====

N/m and Kg/s² are equivalent.
Reply 9
Avatar for CasedIt
CasedIt
OP
thank you so much

DazzYa thank you
Reply 10
Avatar for DazzYaa7
DazzYaa7
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
Reply 11
Avatar for Bilal
Bilal
1
Hey daz speaking to yourself again?
Bilal786
Hey daz speaking to yourself again?

????
Reply 13
Avatar for Bilal
Bilal
1
endeavour
????

It was daz who replied to himself here: 'CasedIt' and 'Dazzzyyya77' are both him. He's a sad case. :biggrin:

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