Question

determine the wavelengh for a transition from the v=0 to the v=1 level .is this tranistion in the ir region of the electromagnetic spectrum?

Answer 1

Answer on Question #76784 - Chemistry - Inorganic Chemistry

Question:

determine the wavelength for a transition from the $v=0$ to the $v=1$ level. Is this transition in the ir region of the electromagnetic spectrum?

Solution:

The photon energy in the transition from the level $v = 0$ to $v = 1$ is:

$$E_{ph} = \Delta E = E_1 - E_0 = \frac{3}{2} h\nu_0 - \frac{1}{2} h\nu_0 = h\nu_0;$$

Since the energy of a photon is given by $E_{\text{photon}} = h\nu$, the frequency of the transition from the first to the next second vibrational level is:

$$E_{ph} = h\nu;$$ $$\lambda = \frac{c}{\nu_0} = \frac{3 \cdot 10^8}{8.963 \cdot 10^{13}} = 3.345 \cdot 10^{-6} \, \text{m} = 3345 \, \text{nm}.$$

Answer: 3345 nm.

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