# How Does the Stiffness of an Interatomic Bond Affect Iron's Elasticity?

• clutch12
In summary, one mole of iron has a mass of 56 grams and a density of 7.87 grams per cubic centimeter. The center-to-center distance between atoms in iron is 2.28 *10^-10 m. A long thin bar of iron with a square cross section of 0.05 cm on a side is hung vertically and a 29kg mass is attached to the bottom, causing the rod to become 1.65 cm longer. Based on these measurements, it is possible to determine the stiffness of one interatomic bond in iron. The number of side-by-side atomic chains in this wire can be calculated to be 4.044 * 10^13.
clutch12

## Homework Statement

One mole of iron (6 *10^23 atoms) has a mass of 56 grams, and its density is 7.87 grams per cubic centimeter, so the center-to-center distance between atoms is 2.28 *10-10 m. You have a long thin bar of iron, 2.9 m long, with a square cross section, 0.05 cm on a side.

You hang the rod vertically and attach a 29 kg mass to the bottom, and you observe that the bar becomes 1.65 cm longer. From these measurements, it is possible to determine the stiffness of one interatomic bond in iron.

How many side-by-side atomic chains (long springs) are there in this wire? This is the same as the number of atoms on the bottom surface of the iron wire. Note that the cross-sectional area of one iron atom is (2.28*10-10)^2 m2

## The Attempt at a Solution

A wire = 2.9 * 5 * 10^-4
= (1.45 * 10^-3 ) ^2
= 2.1025 * 10^-6
A1 atom = (2.28 *10 ^10)^2
= 5.1984 * 10^-20

N chains = Awire/ A1atom
= 2.1025 * 10^-6 / 5.1984 * 10^-20
= 4.044 * 10 ^13

Is this right?

You need the area of the cross section of the wire. What you did calculate is the area of a lateral face. The cross section is a square with a side of 0.5 cm.

so I am multiply 0.5 cm by 0.05 cm?

Area=length*width and L=W. So assuming your post is a typo, 0.5cm x 0.5cm But better yet convert to meters first so the units are the same as others in the problem.

note: .5cm=0.005 meters

Sorry if I confused you. The side of the square is 0.05 cm, according to your problem. I did not read all the zeroes.
So the cross section area is (0.05cm)^2= [5x10^(-4)m]^2

oh so basically i don't need to multiply it by 2.9 then right?

No, you don't. You're trying to determine how many chains of atoms end on the end of the rod, not how many chains end on the side of the rod.

## 1. What is the definition of stiffness of an interatomic bond?

The stiffness of an interatomic bond refers to the resistance of the bond to deformation when subjected to an external force. It is a measure of the strength and rigidity of the bond.

## 2. How is stiffness of an interatomic bond related to bond strength?

The stiffness of an interatomic bond is directly related to the bond strength. A stiffer bond will have a higher bond strength, meaning it will require more energy to break the bond.

## 3. What factors affect the stiffness of an interatomic bond?

The stiffness of an interatomic bond is affected by various factors such as the type of atoms involved, the distance between the atoms, and the bond angle. The type of bonding (ionic, covalent, or metallic) also plays a significant role in determining the stiffness of the bond.

## 4. How is the stiffness of an interatomic bond measured?

The stiffness of an interatomic bond is typically measured using techniques such as atomic force microscopy or nanoindentation. These methods involve applying a known force to the bond and measuring the resulting displacement, which can be used to calculate the stiffness.

## 5. How does temperature affect the stiffness of an interatomic bond?

Temperature can significantly affect the stiffness of an interatomic bond. As temperature increases, the atoms vibrate more, making the bond less stiff. This is because the increased vibrations disrupt the alignment of the atoms, making the bond more susceptible to deformation.

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