Question

The mean distance between the atoms of iron is 3 X ${10}^{-10}$m and interatomic force constant for iron is 7 N $m^{-1}$. The Young's modulus of elasticity for iron is

• A. 2.33 X ${10}^5$ N $m^{-2}$
• B. 23.3 X ${10}^{10}$ N $m^{-2}$
• C. 2.33 X ${10}^9$ N $m^{-2}$
• D. 2.33 X ${10}^{10}$ N $m^{-2}$

Answer 1

The correct option is D 2.33 X ${10}^{10}$ N $m^{-2}$

As we know that,

Interatomic force constant $=$ Young's modulus $\times$ mean atomic distance

$\Rightarrow 7N/m=$ Young's Modulus $\times 3\times {10}^{-10}m$

$\Rightarrow$ Young's modulud $=\frac{7}{3\times {10}^{-10}}N/m^2$

Young's modulus $=2.33\times {10}^{10}N/m^2$

Option $D$ is correct.