NOTE: Part A's answer previously given to me of -2α2x1 + α2x2 is incorrect. Part B's answer previously given to me of -2β2x2 + β2x1 + β2x3 is also incorrect. Can I please be given the correct answer this time? The greenhouse-gas carbon dioxide molecule CO₂strongly absorbs infrared radiation when its vibrationalnormal modes are excited by light at the normal-modefrequencies. CO₂ is a linear triatomic molecule, asshown in (Figure 1), with oxygen atoms of mass mobonded to a central carbon atom of mass mc. Youknow from chemistry that the atomic masses of carbonand oxygen are, respectively, 12 and 16. Assume thatthe bond is an ideal spring with spring constant k.There are two normal modes of this system for whichoscillations take place along the axis. (You can ignoreadditional bending modes.) In this problem, you will findthe normal modes and then use experimental data todetermine the bond spring constant.FigureOmo.1 X1kmc.1x₂k1 of 1mo1 X3Part ALet x₁, x2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net forceon each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt². Carbon has a different mass, so itsnet force is mcd²x/dt². Define a² = k/mo and 3² = k/mc. Find an equation for the second derivative of ₁ coordinate.Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, B.d²x₁dt²=SubmitPart BIVE ΑΣΦ- 2α²x₁ + a²x₂Previous Answers Request AnswerX Incorrect; Try Again; 3 attempts remaining?ReviewFind an equation for the second derivative of ₂ coordinate.Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, B.

Question

NOTE: Part A's answer previously given to me of -2α2x1 + α2x2 is incorrect. Part B's answer previously given to me of -2β2x2 + β2x1 + β2x3 is also incorrect. Can I please be given the correct answer this time? The greenhouse-gas carbon dioxide molecule CO₂strongly absorbs infrared radiation when its vibrationalnormal modes are excited by light at the normal-modefrequencies. CO₂ is a linear triatomic molecule, asshown in (Figure 1), with oxygen atoms of mass mobonded to a central carbon atom of mass mc. Youknow from chemistry that the atomic masses of carbonand oxygen are, respectively, 12 and 16. Assume thatthe bond is an ideal spring with spring constant k.There are two normal modes of this system for whichoscillations take place along the axis. (You can ignoreadditional bending modes.) In this problem, you will findthe normal modes and then use experimental data todetermine the bond spring constant.FigureOmo.1 X1kmc.1x₂k1 of 1mo1 X3Part ALet x₁, x2, and 3 be the atoms' positions measured from their equilibrium positions. First, use Hooke's law to write the net forceon each atom. Pay close attention to signs! For each oxygen, the net force equals mod²x/dt². Carbon has a different mass, so itsnet force is mcd²x/dt². Define a² = k/mo and 3² = k/mc. Find an equation for the second derivative of ₁ coordinate.Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, B.d²x₁dt²=SubmitPart BIVE ΑΣΦ- 2α²x₁ + a²x₂Previous Answers Request AnswerX Incorrect; Try Again; 3 attempts remaining?ReviewFind an equation for the second derivative of ₂ coordinate.Express your answer in terms of some, all, or none of the variables ₁, 2, 3, and the constants a, B.

Accepted Answer

Answered: Image /qna-images/answer/73f9635f-2a0e-4a68-86fc-b208a8ac24a5.jpg