One mole of titanium (6 1023 atoms) has a mass of 48 grams, and its density is 4.54 grams per cubic centimeter, so the center-to-center distance between atoms is 2.60 10-10 m. You have a long thin bar of titanium, 2.4 m long, with a square cross section, 0.11 cm on a side.

You hang the rod vertically and attach a 76 kg mass to the bottom, and you observe that the bar becomes 1.23 cm longer. From these measurements, it is possible to determine the stiffness of one interatomic bond in titanium.

What is the stiffness of a single interatomic "spring"?

  1. 👍 0
  2. 👎 0
  3. 👁 1,225
asked by hannah
  1. The force applied to the bar is 34*9,8 = 333.2 N. The extension of the wire ∆L = 0.0145 m, so the bar stiffness is F/∆L = 2.30*10^4 N/m

    The number of atoms in one layer of cross section is area of the bar divided by the area of one atom =0.0012²/(2.84*10^-10)² = 1.785*10^13.

    No no of bonds along the length is 2.5/(2.84*10^-10) = 8.80*10^9

    The applied force is divided among all the bonds along the length, and then divided among all the atoms in a cross-section layer The force applied to each atom in a layer is then 333.2/(1.785*10^13*8.80*10^9) = 2.12*10^-21 N

    The strain (fractional length increase, ∆L/L) on the bar is 0.0145/2.5 = 0.0058. This will also be the strain between the atom layers. The bond extension ∆L is then 2.84*10^-10 * 0.0058 = 1.6472*10^-12 m. The bond stiffness F/∆L = (2.12*10^-21)/(1.6472*10^-12) = 1.29*10^-9 N/m

    1. 👍 0
    2. 👎 2
    posted by BOB

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A hanging wire made out of titanium with diameter 0.080 cm is initially 2.3 m long. When a 78 kg mass is hung from it, the wire stretches an amount 2.89 cm. A mole of titanium has a mass of 47.9 grams, and its density is 4.51

    asked by Amelie on February 25, 2011
  2. Chemistry (Check)

    Classify each of these statements as always true, sometimes true, or never true 1)___AT_____A mole of a pure substance contains 6.02 X 1023 atoms. 2)____ST____The representative particle of a compound is the molecule.

    asked by bryan on February 6, 2007
  3. Chemistryy.

    Some mole problems! Which quantity of neon may be represented by the symbol Ne? A) 1 gram B) 4 liters C) 6 x 1023 atoms D) 2 moles A sample of nitrogen containing 1.5 x 1023 molecules has the same number of molecules as a sample

    asked by Jenny on June 6, 2011
  4. math

    What is one mole of H2O composed of? A. 2 hydrogen atoms and 1 oxygen atom B. 2 × (6.02 × 1023) hydrogen atoms and 6.02 ×1023 oxygen atoms C. 3 atoms of water and 2 oxygen molecules D. one half of a molecule of peroxide I say A

    asked by shana on November 8, 2012
  5. Chemistry

    I did the question but I need help is this right? Thanks How many atoms of chlorine are in 19.0 grams of MgCl2? 24.3 + 2(35.5) = 95.3 19.0/95.3 x 6.022 x 1023 = 1.201 1023

    asked by Shine Bright Shine Far on December 3, 2018
  1. Chem 101. Science

    Rank the following samples in mass from least to greatest. a) 2 x 1023 S atoms b) 0.25 mol of Cu atoms c) 2 mol of N atoms d) 6 x 1023 Na atoms

    asked by Samuel on August 26, 2010
  2. Chemistry

    Posted by Angeline on Monday, April 20, 2009 at 5:35pm. A few many grams are in 48.7x10^24? I don't know how to convert atoms to grams. I can do moles to grams or moles to atoms, but not atoms to grams. My other

    asked by Angeline on April 20, 2009
  3. chemistry

    Hi, how many moles does 0.225g of oxygen atoms represent? If 1 mole of oxygen atoms represents 16.0g? Thanks mols = grams/molar mass. thot so. Thanks for confirming ;) This is right for oxygen atoms, however, oxygen in the

    asked by bertie on February 5, 2007
  4. Density of Gas at STP

    Hi Can anyone explain how to calculate the density in g l -1 of a gaseous oxide at STP. I don't understand the term g l -1 !! Thank You "g l-1" should have the -1 as a superscript, meaning g l^-1, or g/l. It means they want the

    asked by Freddo on January 24, 2007
  5. physics

    We want to find how much charge is on the electrons in a nickel coin. Follow this method. A nickel coin has a mass of about 4 g. Find the number of atoms in a nickel coin. Each mole (6.02 × 1023 atoms) has a mass of about 57.9 g.

    asked by help on March 11, 2020

More Similar Questions