Question 138: Oscillations

Question

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = 6.02 × 1023 gm mole–1)

Accepted Answer

6.02 $$ 	imes $$ 10
23
atoms of silver = 108 gm
1   atoms   of   silver   =   $${{108 	imes {{10}^{ - 3}}} \over {6.02 	imes {{10}^{23}}}}$$ kg
For a harmonic oscillator
f = $${1 \over {2\pi }}$$ $$\sqrt {{k \over m}} $$
Where  k = force constant
$$ \Rightarrow $$$$\,\,\,$$ f
2
= $${1 \over {4{\pi ^2}}}$$ $$\left( {{k \over m}} ight)$$
$$ \Rightarrow $$$$\,\,\,$$ k = mf
2
$$ 	imes $$ 4$$\pi $$
2
Given,
f = 10
12
m = $${{108 	imes {{10}^{ - 3}}} \over {6.02 	imes {{10}^{23}}}}$$
$$	herefore\,\,\,$$ k = $${{108 	imes {{10}^{ - 3}}} \over {6.02 	imes {{10}^{23}}}}$$ $$ 	imes $$ 10
12
$$ 	imes $$ 4$$\pi $$
2
= 7.1 N/m

Answer

5.5 N/m

Answer

6.4 N/m

Answer

7.1 N/m

Answer

2.2 N/m

Oscillations

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = 6.02 × 1023 gm mole–1)

Choose the correct answer: