An atom in a solid vibrates at 10 THz with amplitude 11 pm Part A: Find the atom

Question

An atom in a solid vibrates at 10 THz with amplitude 11 pm

Part A: Find the atom's maximum speed. Express your answer to two significant figures and include the appropriate units.

Part B: Find the atom's maximum acceleration. Express your answer to two significant figures and include the appropriate units.

Part C: If it's a carbon atom, what's its energy? Express your answer to two significant figures and include the appropriate units

Note 2 people got this wrong already...this should help...In part A) Make sure that you have the correct factors for the prefixes (THz = 10^12Hz, pm = 10^-12m). If you get part A correct, then you would most probably get part B correct.

In part C) Compute (1/2)mv^2 for the total energy. You need the mass of carbon-12 atom in kg(The textbook, Appendix A-7, gives it in atomic mass unit). The mass of carbon-12 atom is the same as 12 times the mass of proton.

Explanation / Answer

A)
f = 10 THz
= 1*10^13 Hz

w = 2*pi*f
= 2*pi*(1*10^13)
=6.283*10^13 rad/s
A = 11 pm = 11*10^-12 m
Vmax = A*w
= (11*10^-12)*(6.283*10^13)
=690 m/s

B)
amax = A*w^2
= (11*10^-12)*(6.283*10^13)^2
= 4.3*10^16 m/s^2

C)
m of carbon atom = 1.994*10^-26 Kg
total energy = maximum kinetic energy
= 0.5*m*Vmax^2
= 0.5*(1.994*10^-26)*(690)^2
=4.7*10^-21 J

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