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Question: The Young’s modulus for steel is \(Y = 2 \times 10^{11}N/m^{2}\). If the inter-atomic distance is 3....

The Young’s modulus for steel is Y=2×1011N/m2Y = 2 \times 10^{11}N/m^{2}. If the inter-atomic distance is 3.2Å, the inter atomic force constant in N/ Å will be

A

6.4×1096.4 \times 10^{9}

B

6.4×10−96.4 \times 10^{- 9}

C

3.2×1093.2 \times 10^{9}

D

3.2×10−93.2 \times 10^{- 9}

Answer

6.4×10−96.4 \times 10^{- 9}

Explanation

Solution

k=Y×r0=2×1011×3.2×10−10=6.4×101N/mk = Y \times r_{0} = 2 \times 10^{11} \times 3.2 \times 10^{- 10} = 6.4 \times 10^{1}N/m = 6.4×10−9N/A˚6.4 \times 10^{- 9}N/Å.