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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?

2.2N/m

5.5N/m

7.1N/m

6.4N.m

Solution:

Time period of SHM is given by: T = 2π√(m/k)
Frequency = 1/(2π√(m/k)) = 10¹²
where m = mass of one atom = 108/(6.02 × 10²³ × 10⁻³ ) kg
1/(2π√(m/k)) = 10¹²
k = 7.1 N/m