A silver atom in a solid oscillates in simple | vedclass

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(A) The frequency of an atom in $SHM$ is given by the formula: $f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$,where $k$ is the force constant and $m$ is the

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(A) The frequency of an atom in $SHM$ is given by the formula: $f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$,where $k$ is the force constant and $m$ is the mass of one silver atom.The mass of one silver atom is calculated as: $m = \frac{	ext{Molar mass}}{	ext{Avogadro number}} = \frac{108 	imes 10^{-3} \ kg/mol}{6.02 	imes 10^{23} \ mol^{-1}} \approx 1.794 	imes 10^{-25} \ kg$.Given $f = 10^{12} \ s^{-1}$,we rearrange the formula to solve for $k$: $k = m(2\pi f)^2$.Substituting the values: $k = (1.794 	imes 10^{-25}) 	imes (2 	imes 3.1416 	imes 10^{12})^2$.$k = (1.794 	imes 10^{-25}) 	imes (39.478 	imes 10^{24}) \approx 7.08 \ N/m$.Rounding to one decimal place,we get $k = 7.1 \ N/m$.

$A$ silver atom in a solid oscillates in simple harmonic motion in a specific direction with a frequency of $10^{12} \ s^{-1}$. What is the force constant of the bonds connecting one atom to the others? (Molar mass of silver $= 108 \ g/mol$ and Avogadro number $= 6.02 \times 10^{23} \ mol^{-1}$)

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