A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 10 12 s - 1 . What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver, = 108 g mol - 1 and Avogadro number = 6.02 × 10 23 )

Step-by-step solution

Given, molecular weight of silver M = 108   g and Avogadro's number N A = 6 . 02 × 10 23 , frequency f = 10 12   s . Mass of single silver atom will be given by, m = M N = 108 6 . 02 × 10 23 = 1 . 79 × 10 - 22   g = 1 . 79 × 10 - 25   kg The bonds between the atoms can be considered as spring and then using the spring analog, the time period of the oscillation of the atoms is given by, T = 1 f = 2 π m k ; where k is spring constant. 1 10 12 = 2 π 1 . 79 × 1