Calculate CO bond length from J=0 to J=1 transition

[cep]

Homework Statement

The J=0 to J=1 transition fro 12C16O carbon monoxide occurs at 1.153x10⁵ MHz. Calculate the value of the bond length in CO.

Homework Equations

2B = h/(4π²I)

μ = m1*m2/(m1+m2)

I = μr²

The Attempt at a Solution

I = 6.61x10^-34/ (4*π²*1.153x10⁸) = 1.45x10^-43 kg m²

μ = 12.01*16.00/(12.01+16.00) *1.661x10^-27 = 1.14x10^-26kg

r = √(I/μ) = √(1.45x10^-43/1.14x10^-26) = 2.52x10^-9 m or 2520 pm, which is significantly larger than the observed value of 113 pm.

Does anyone see where I went wrong?

Thanks!

 

[Borek]

2B = h/(4π²I)

My QM is so rusty I am trying to not touch it as it may fell apart, but I just checked in wikipedia and it is either

$$\bar B = \frac {h} {8\pi^2cI}$$

or

$$B = \frac {\hbar} {2I}$$

Neither fits what you wrote.

 

[cep]

I've tried both of those-- still orders of magnitude too large.

 

[B. Richter]

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!

 

[radiator]

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