A hanging iron wire with diameter 0.05 cm is initially 1.8 m long. When a 60 kg mass is hung from it, the wire stretches an amount 2.55 cm. A mole of iron has a mass of 56 g, and its density is 7.87 g/cm3.(a) What is the length of an interatomic bond in iron (diameter of one atom)?  (b) what is the approximate value of the effective spring stiffness of one interatomic bond in iron?

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Asked Sep 29, 2019
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A hanging iron wire with diameter 0.05 cm is initially 1.8 m long. When a 60 kg mass is hung from it, the wire stretches an amount 2.55 cm. A mole of iron has a mass of 56 g, and its density is 7.87 g/cm3.

(a) What is the length of an interatomic bond in iron (diameter of one atom)?
  

(b) what is the approximate value of the effective spring stiffness of one interatomic bond in iron?
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Expert Answer

Step 1

(a) The length of interatomic bond in iron is

1/3
V
а-
NA
4
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1/3 V а- NA 4

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Step 2

The volume can be defined as

т
[2]
V
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Image Transcriptionclose

т [2] V

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Step 3

Use the equation (2) in (1) to find the le...

/3
тр
а-
NA
1/3
(56g)/(7.87g mol/cm3)
(6.022 x1023 atoms/mol)
2.28x10% cm
-22.8nm
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/3 тр а- NA 1/3 (56g)/(7.87g mol/cm3) (6.022 x1023 atoms/mol) 2.28x10% cm -22.8nm

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Mechanical Properties of Matter

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