Answer to Question #123851 in Material Science Engineering for Praveen

Question

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.

Answer 1

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

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

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

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