HCl Energy and Angular Momentum ?

[Rick2015]

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?

 

[Quantum Defect]

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"

 

[Rick2015]

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

 

[Quantum Defect]

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

 

[Rick2015]

B = hbar^2 / 2 I