The bulk of modulus of a metal is `10^(10)(N)/(m^2)` and Poisson's ratio `0.20`. If average distance between the molecules is `3Å` the the interatomic force constant is

Options

A. `30(N)/(m)`
B. `75(N)/(m)`
C. `7.5(N)/(m)`
D. `5.4(N)/(m)`

Answer

A

Explanation

The relation between bulk modulus `K`, Poisson's ratio `tau` and Young's modulus `Y` is
`Y=3K(1-2sigma)`
Given, `K=10^(10)(N)/(m^2)`, `sigma=0.2`
`Y=3xx10^(10)(1-2xx0.2)`
`=1.8xx10^(10)(N)/(m^2)`
Interatiomic force constant is
`K=Yr=1.8xx10^(10)xx3xx10^(-10)`
`K=5.4(N)/(m)`