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In this lesson, we will learn how to calculate molecular rotational and vibrational energies, atomic equilibrium separations, and dissociation energies.

Q1:

The characteristic energy of the N_{2} molecule is 2 . 4 8 × 1 0 − 4 eV. Determine the separation distance between the nitrogen atoms.

Q2:

Find the equilibrium separation distance between the Na^{+} and F^{−} ions in an NaF crystal. Use a value of 41.99 g/mol for the molar mass of NaF and use a value of 2.56 g/cm^{3} for the density of an NaF crystal.

Q3:

The separation between hydrogen atoms in a H_{2} molecule is about 0.075 nm. Determine the characteristic energy of rotation in eV. Use a value of 1 . 0 5 × 1 0 − 3 4 Js for the value of the Reduced Planck Constant, and a value of 931.5 MeV/c^{2} for the value of the unified atomic mass unit.

Q4:

The crystal structure of caesium iodide is body-centered cubic. A C s + ion occupies a cubic volume of 𝑟 3 0 , where 𝑟 0 is the equilibrium separation of ions in the crystal. What is the distance of a C s + ion to its “nearest neighbor” I – ion if 𝑟 = 0 . 4 6 0 n m ?

Q5:

A diatomic F_{2} molecule with an equilibrium separation of 0.14 nm is in the 𝑙 = 1 state.

What is the energy of the molecule?

How much energy is radiated in a transition from a 𝑙 = 2 to a 𝑙 = 1 state?

Q6:

An H_{2} molecule with an equilibrium separation distance of 0.0750 nm can have various rotational energy states.

Determine the rotational energy of the 𝑙 = 0 state.

Determine the rotational energy of the 𝑙 = 1 state.

Determine the rotational energy of the 𝑙 = 2 state.

Q7:

A molecule oscillates at a frequency of 88 THz. What is the difference between its adjacent energy levels?

Q8:

The separation between nitrogen atoms in an N 2 molecule is 0.11 nm. Determine the characteristic energy of rotation in electron volts. Use a value of 14 u for the atomic mass of N 2 .

Q9:

The potential energy of a crystal is − 9 . 1 0 eV per ion pair. Find the dissociation energy for three moles of the crystal.

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