Q40E Starting with equation (10-4), s... [FREE SOLUTION]

Chapter 10: Q40E (page 469)

Starting with equation (10-4), show that if $螖苍$ is $- 1$ as a photon is emitted by a diatomic molecule in a transition among rotation-vibration states, but $螖鈩�$ can be $卤 1$ . Then the allowed photon energies obey equation (10-6).

Short Answer

Expert verified

The photon鈥檚 energy is equal to $E_{photon} = h \sqrt{\frac{魏}{渭}} 卤 1 \frac{h^{2}}{{渭补}^{2}}$ .

Step by step solution

Calculate the energy change for a molecule

Let us calculate the energy change for a molecule changing from state n,l to state n-1, l+1, this is the photons energy.

$\begin{matrix} E_{nl} 鈭� E_{n 鈭� l, l + 1} = (n + \frac{1}{2}) h \sqrt{\frac{魏}{渭}} + \frac{h^{2} 脳 l 脳 (l + 1)}{2 {渭补}^{2}} 鈭� ((n 鈭� 1 + \frac{1}{2}) h \sqrt{\frac{魏}{渭}} + \frac{h^{2} 脳 (l + 1) 脳 (l + 2)}{2 {渭补}^{2}}) \\ = h \sqrt{\frac{魏}{渭}} + \frac{h^{2} 脳 (l 鈭� (1 + 2)) 脳 (l + 1)}{2 {渭补}^{2}} \\ = h \sqrt{\frac{魏}{渭}} 鈭� \frac{h^{2} 脳 (l + 1)}{{渭补}^{2}} \end{matrix}$

Then let us calculate the energy change for a molecule changing from state n,l to state n-1,l-1. This is the photon鈥檚 energy.

$\begin{matrix} E_{nl} 鈭� E_{n 鈭� l, l 鈭� 1} = (n + \frac{1}{2}) h \sqrt{\frac{魏}{渭}} + \frac{h^{2} 脳 l 脳 (l + 1)}{2 {渭补}^{2}} 鈭� ((n 鈭� 1 + \frac{1}{2}) h \sqrt{\frac{魏}{渭}} + \frac{h^{2} 脳 (l 鈭� 1) 脳 (l)}{2 {渭补}^{2}}) \\ = h \sqrt{\frac{魏}{渭}} + \frac{h^{2} 脳 (l + 1 鈭� (l 鈭� 1)) 脳 (1)}{2 {渭补}^{2}} \\ = h \sqrt{\frac{魏}{渭}} 鈭� \frac{h^{2} 脳 l}{{渭补}^{2}} \end{matrix}$

Conclusion.

Thus the photon鈥檚 energy is equal to

$\begin{matrix} E_{photon} = h \sqrt{\frac{魏}{渭}} 卤 1 \frac{h^{2}}{{渭补}^{2}} \\ I = 1, 鈥� 2, 鈥� 3, .......... \end{matrix}$

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Starting with equation (10-4), show that if $螖苍$ is $- 1$ as a photon is emitted by a diatomic molecule in a transition among rotation-vibration states, but $螖鈩�$ can be $卤 1$ . Then the allowed photon energies obey equation (10-6).

Short Answer

Step by step solution

Calculate the energy change for a molecule

Conclusion.

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91影视

Starting with equation (10-4), show that if 螖苍 is-1 as a photon is emitted by a diatomic molecule in a transition among rotation-vibration states, but 螖鈩�can be卤1 . Then the allowed photon energies obey equation (10-6).

Short Answer

Step by step solution

Calculate the energy change for a molecule

Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

Work Energy and Power

Magnetism and Electromagnetic Induction

Magnetism

Conservation of Energy and Momentum

Radiation

Study anywhere. Anytime. Across all devices.

Starting with equation (10-4), show that if $螖苍$ is $- 1$ as a photon is emitted by a diatomic molecule in a transition among rotation-vibration states, but $螖鈩�$ can be $卤 1$ . Then the allowed photon energies obey equation (10-6).