Distance between the atoms in HCl

[skrat]

Homework Statement

At transition from first excited state of rotator to ground state the molecule of HCl shoots out a photon with ##4,8\cdot 10^{-4}m##. How far apart are the atoms in the molecule?

Homework Equations

The Attempt at a Solution

What is wrong with:

##\Delta E=E_\gamma ##

##\frac{\hbar ^2}{2m_rr^2}|l_f(l_f+1)-l_i(l_i+1)|=\frac{hc}{\lambda }##

Where ##f## indicates final state and ##i## for initial state and ##m_r=\frac{1\cdot 35.45}{1+35.45}=0,97au##.

##l_f=0## and ##l_i=1##, which gives me

##\frac{\hbar ^2}{2m_rr^2}(2)=\frac{hc}{\lambda }##

and finally

##r=\sqrt{\frac{hcm_rc^2}{\lambda \hbar ^2c^2}}=7.64 nm## instead of ##0.13 nm##.

What am I doing wrong here?

 

[kontejnjer]

Your reasoning is correct, however your expression for [itex]r[/itex] seems to be off, I get:
[itex]r=\sqrt{\frac{h\lambda}{4π^{2}mc}}[/itex]
which yields the desired answer.

 

[skrat]

Ah, of course... My result is actually ##r^{-1}##. Thanks for that!