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 Avagadro number = 6.02 × 10²³ gm mole^–1)

5.5 N/m

6.4 N/m

7.1 N/m

2.2 N/m

Solution

7.1 N/m

Given frequency f = 10¹²/sec

Angular frequency ω = 2πf = 2π x 10¹² /sec
Force constant k = mω²

= $\frac{108 x 10^{- 3}}{6.02 x 10^{23}} x 4 π^{2} x 10^{24} k = 7.1 N / m$

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