**Q1. P3**(a) Suppose that you measure the lowest-energy rotational transition for \(^{16}\text{OH}\) at a frequency of \(37.742 \, \text{cm}^{-1}\). What is the bond length in units of pm? (*Show calculation*)(b) Suppose that you have a symmetric rotor with rotational constants: \(A = 125 \, \text{cm}^{-1}\) \(B = 100 \, \text{cm}^{-1}\) (*HINT: Recall that A is the coefficient along the unique direction.*) Assuming that the excitation laser is at \(10,000 \, \text{cm}^{-1}\), calculate all the Anti-Stokes lines involving the \(J = 0\), \(J = 1\), and \(J = 2\) states.

16O1H is a diatomic molecule for which the rotational energy is given as: E=BJ(J+1) For lowest-energy transition, transition occurs from J = 0 to J= 1 level, so energy corresponding to this transition: ∆E=B(1)(1+1)-B(0)(0+1)∆E=2B=2×h8πIc37.742 cm-1=2×6.626×10-34 J.s8×3.14×I×3×1010 cm/sI=46.59×10-48 kg.m2 (1 J= 1 kg.m2.s-2) The moment of inertia of the molecule is given as: I=μr2----(2) Reduced mass of the moleculeμ=mOmH(mO+mH)μ=16×1 amu2(16+1) amu=1617 amuμ=1617×1.66×10-27 kgμ=1.56×10-27 kgUsing equation (2): 46.59×10-48 kg.m2=1.56×10-27 kg.r2r2=29.86 m2r=172.8×10-12 mr=172.8 pm Ans: Bond length = 172.8 pm

Answered: (a) Suppose that the you measure the…

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Chemistry

(a) Suppose that the you measure the lowest-energy rotational transition for 160'H at a frequency of 37.742 cm-!. What is the bond length in units of pm? (Show calculation)

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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