HCl Energy and Angular Momentum ?

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Discussion Overview

The discussion revolves around calculating the energy and angular momentum of the first nonzero rotational state of HCl, a diatomic molecule. Participants explore the relevant equations and concepts related to rotational energy levels and angular momentum in quantum mechanics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant states the bond distance for HCl is 1.29 A and questions the approach to finding energy and angular momentum for the first nonzero rotational state.
  • Another participant corrects the initial approach, suggesting the energy levels for a rigid rotor are given by E = B*J*(J+1) and mentions the need to calculate the rotational constant B using the bond distance and reduced mass.
  • A participant expresses confusion regarding the calculation of angular momentum, noting that for J = 1, M can take values of -1, 0, or 1, and questions the resulting value of Lz.
  • Another participant reiterates that the equation for B is incorrect and emphasizes that angular momentum is quantized in units of h-bar.
  • One participant provides a formula for B as B = hbar^2 / 2 I.

Areas of Agreement / Disagreement

Participants do not reach consensus on the correct equations for B and the calculations for angular momentum, indicating ongoing disagreement and confusion regarding the approach to the problem.

Contextual Notes

There are limitations in the discussion regarding the assumptions made in the calculations, the dependence on the definitions of terms like the rotational constant, and unresolved mathematical steps in deriving the energy and angular momentum.

Rick2015
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The bond distance for HCl is 1.29 A. At the lowest rotational state the energy is zero.
What is the energy and angular momentum Lz corresponding to the first nonzero rotational state?

I m not sure if I am approaching this problem right.
first I did 1.2 A = 8.3 x 10^7 cm^-1
Then I used this equation for energy because HCl has characteristic of diatomic molecule.
E = (v cm^-1)hc100
is this right?
 
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Rick2015 said:
The bond distance for HCl is 1.29 A. At the lowest rotational state the energy is zero.
What is the energy and angular momentum Lz corresponding to the first nonzero rotational state?

I m not sure if I am approaching this problem right.
first I did 1.2 A = 8.3 x 10^7 cm^-1
Then I used this equation for energy because HCl has characteristic of diatomic molecule.
E = (v cm^-1)hc100
is this right?

This is not right.

The energy levels for a rigid rotor look like:

E = B*J*(J+1), where B is the rotational constant.

You can calculate B using the bond distance and the reduced mass. For Cl there are two isotopes with significant natural occurrences.

For the lowest level, J=0, E=0.

Angular momentum is similar.

Wikipedia has an ok discussion of this. Google "rigid rotor energy levels"
 
Ok. Thanks
So B = hbar/2I
And for the angular momentum: Lz = Mj hbar
but if J = 1 ; M = -1, 0, 1 right?
lost again? because if I just use 1 I will have Lz = hbar
 
Rick2015 said:
Ok. Thanks
So B = hbar/2I
And for the angular momentum: Lz = Mj hbar
but if J = 1 ; M = -1, 0, 1 right?
lost again? because if I just use 1 I will have Lz = hbar

Your equation for B is still not correct...
Angular momentum is quantized in units of h-bar
 
B = hbar^2 / 2 I
 

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