Answer to Question #123851 in Material Science Engineering for Praveen

Question #123851
Estimate the Young’s modulus of a material. Given r0=2.5 Å, n = 1, m = 9, and A = 7.68×10–29 J m.
1
Expert's answer
2020-07-02T05:54:50-0400

Here it is given "r_0=2.5 A^o=2.5 \\times 10 ^{-10} m" ,n=1,m=9, and A= "7.68\\times 10^{-29}"

we know that ,

"b=\\frac{A\\times ( r_0^8)}{9}= \\frac{7.68 \\times 10 ^{-29}\\times (2.5\\times 10 ^{-10})^8}{9}"

"b=1.30\\times 10 ^{-106}"

"y=\\frac{((-2\\times A\\times r_0^8)+(90\\times b))}{r_o^{11}}= \\frac{( 2.34 \\times 10^{-105})+(11.7\\times 10 ^{-105})}{(2.5\\times 10^{-10})^{11}}=\\frac{14.04 \\times 10^{-105}}{2.38\\times ^{-106}}"

"y=0.5899"

and young's modulus

"E=\\frac{y}{r_0}=\\frac{0.5899}{2.5 \\times 10^{-10}}" \

"E=0.235966 \\times 10 ^{10}"

"E=235.966\\times 10 ^7" "\\frac{N}{mm^2}"


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