How Far Apart Are 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 $r$ seems to be off, I get:
$r=\sqrt{\frac{h\lambda}{4π^{2}mc}}$
which yields the desired answer.

 

[skrat]

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