Homework Help: Calculate CO bond length from J=0 to J=1 transition

Even though this is an old question I figured I'd post an answer for people who might have the same question and end up here.

The rotational energy for a specific level J, E_J = J(J+1)[((m₁ + m₂)*h²)/(8m₁m₂R²) = J(J+1)B

In this case B = ((m₁ + m₂)*h²)/(8m₁m₂R²)

The transition from J = 0 → J = 1 then would be [1(1+1)B] - [0(0+1)B] = 2B

1.153x10⁵ MHz is 1.153x10¹¹ Hz. Solving for E from E = hv where h is still planck's constant and v is the frequency gives 7.64x10^-23 Joules which is equal to 2B as shown above.

7.64x10^-23 Joules = 2B = 2[((m₁ + m₂)*h²)/(8m₁m₂R²)]

From here you just manipulate the equation to solve for R then plug in the values for m₁, m₂, E, and h. The value for R (not a radius mind you, but a bond length) should be ~115.3 pm.

Oh and if you still aren't getting the right answer, make sure the check your units!

 

You were right only missed a factor of 3 by 1.153x10^11, the rest check your calculator. I know its been a while