Question

The Young's modulus for steel is $Y=2\times {10}^{11}N/m^2.$ If the inter-atomic distance is $3.2A$ the inter atomic force constant in N/A will be

• A. $6.4\times {10}^9$
• B. $6.4\times {10}^{-9}$
• C. $3.2\times {10}^9$
• D. $3.2\times {10}^{-9}$

Answer 1

The correct option is B $6.4\times {10}^{-9}$

As inter atomic forces are electrical in nature , they do not follow the coulomb's law ;.

As distance between two atom is L, then area of one chain of atoms = L\timesL= $L^2$

Y= $F/A\times L/L$=$F/L\times L/A$ $=\text{Force constant}\times$ $\frac{L}{L^2}$ ;

$F.C=Y\times L$

Interatomic stress = Youngs module \times strain ;

Stress= $2\times {10}^{11}\times 3.2\times {10}^{-10}$ = 64 $N^{-m}$ ;

So, force constant for angstrom length = $64\times {10}^{-10}$

= $6.4\times {10}^{-9}$ .