91影视

The given data can be listed below as-

• The mass of the object is = 14 kg.
• The atomic weight of the object is =197 g/mol.
• The density of the object is $蚁=19.3g/c{m}^3$.
• The length of the object is L=2.5m.
• The radius of the object is$r=1mm=1脳{10}^{3}m$.
• The change in the length of the object is$鈭�L=0.00139m$

The ratio of the stress and the strain of an object gives the value of the Young鈥檚 modulus.

The equation of the Young鈥檚 modulus gives the Young鈥檚 modulus and the interatomic spring stiffness.

the equation of the Number of moles in the wire is,

$n=\frac{m}{mw}$

Here, n is the number of moles, mw is the atomic weight

Substituting the values in the above equation,

$$\begin{gathered} n=\frac{14脳{10}^{3}g}{197g/mole} \\ =71.659mol \end{gathered}$$

The equation of the number of atoms is expressed as,

$N=n脳N_A$

Here, N is the number of Atoms, n is the number of moles and is the Avogadro's number

Substituting the values in the above equation,

$$\begin{gathered} N=71.06mol脳6.023脳{10}^{23} \\ =4.27脳{10}^{25}mol\left[N_A=6.023脳{10}^{23}\right] \end{gathered}$$

The equation of the interatomic bond length can be expressed as-

$d={\left(\frac{ml蚁}{N}\right)}^{\frac{1}{3}}$

Here, d is the interatomic bond length and$蚁$is the density

Substituting the values in the above equation,

$$\begin{gathered} d=\left(\frac{14脳{10}^{3}g}{4.27脳{10}^{25}mol脳19.3g/c{m}^3}\right) \\ =2.56脳{10}^{-8}cm \end{gathered}$$

or

$=2.56脳{10}^{-10}m$

The equation of the Young鈥檚 modulus of the wire is,

$$\begin{gathered} Y=\frac{Stress}{Strain} \\ =\frac{F}{A}脳\frac{L}{鈭�L} \end{gathered}$$

Y is the Young鈥檚 modulus,$鈭�l$ = change in length, F= force applied load (load), L = original length and A= Cross sectional area

Substituting the values in the above equation,

$$\begin{gathered} Y=\frac{14kg脳9.8m/s^2}{3.14脳{\left({10}^{-3}m\right)}^2}脳\frac{2.5}{1.39脳{10}^{-3}m} \\ =7.85脳{10}^{10}N/m^2 \end{gathered}$$

Thus, the Young鈥檚 modulus for the wire is$=7.85脳{10}^{10}N/m^2$.

b)

The equation of the interatomic spring stiffness is,

$k_s=Yd$

Here, $k_s$is the interatomic spring stiffness, Y and d are the Young鈥檚 modulus and the density respectively.

Substituting the values in the above equation,

$k=7.85脳{10}^{10}N/m^2脳2.56脳{10}^{-10}m$

$=20.096N/m$

Thus, the interatomic spring stiffness for gold is$20.096N/m$.