Question

The Young’s modulus for steel is 2.0 x 10 11 N/m 2 and the interatomic spacing is 2.6A . Find the increase in inter atomic spacing, when a steel wire is subjected to a stress of 5 x 10 9 N/m

Answer 1

Increase in Atomic Spacing = 6.5 x 10⁻¹² m = 6.5 pm

Step-by-step explanation:

The young's modulus of a material is given by the following formula:

Young's Modulus = Stress/Strain

2 x 10¹¹ N/m² = (5 x 10⁹ N/m²)/Strain

Strain = (5 x 10⁹ N/m²)/(2 x 10¹¹ N/m²)

Strain = 0.025

Now, the formula for the strain in the steel wire can be written in terms of atomic spacing as follows:

Strain = Increase in Atomic Spacing/Initial Atomic Spacing

0.025 = Increase in Atomic Spacing/2.6 °A

Increase in Atomic Spacing = (0.025)(2.6 x 10⁻¹⁰ m)

Increase in Atomic Spacing = 6.5 x 10⁻¹² m = 6.5 pm