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Worksheet: Molecular Energy Levels

Q1:

The characteristic energy of the N2 molecule is 2 . 4 8 Γ— 1 0 βˆ’ 4 eV. Determine the separation distance between the nitrogen atoms.

Q2:

A diatomic F2 molecule with an equilibrium separation of 0.14 nm is in the 𝑙 = 1 state.

What is the energy of the molecule?

  • A 2 . 8 Γ— 1 0 βˆ’ 4 eV
  • B 2 . 4 Γ— 1 0 βˆ’ 4 eV
  • C 3 . 0 Γ— 1 0 βˆ’ 4 eV
  • D 2 . 2 Γ— 1 0 βˆ’ 4 eV
  • E 3 . 3 Γ— 1 0 βˆ’ 4 eV

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

  • A 4 . 4 Γ— 1 0 βˆ’ 4 eV
  • B 4 . 6 Γ— 1 0 βˆ’ 4 eV
  • C 4 . 2 Γ— 1 0 βˆ’ 4 eV
  • D 3 . 8 Γ— 1 0 βˆ’ 4 eV
  • E 4 . 9 Γ— 1 0 βˆ’ 4 eV

Q3:

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

Q4:

Find the equilibrium separation distance between the Na+ and Fβˆ’ 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/cm3 for the density of an NaF crystal.

Q5:

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 .

  • A 2 . 0 Γ— 1 0 βˆ’ 4 eV
  • B 1 . 5 Γ— 1 0 βˆ’ 4 eV
  • C 1 . 8 Γ— 1 0 βˆ’ 4 eV
  • D 2 . 5 Γ— 1 0 βˆ’ 4 eV
  • E 5 . 7 Γ— 1 0 βˆ’ 4 eV

Q6:

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

Q7:

An H2 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.

  • A 1 . 4 9 Γ— 1 0 βˆ’ 2 eV
  • B 1 . 4 0 Γ— 1 0 βˆ’ 2 eV
  • C 1 . 2 6 Γ— 1 0 βˆ’ 2 eV
  • D 1 . 1 4 Γ— 1 0 βˆ’ 2 eV
  • E 1 . 6 1 Γ— 1 0 βˆ’ 2 eV

Determine the rotational energy of the 𝑙 = 2 state.

  • A 4 . 0 4 Γ— 1 0 βˆ’ 2 eV
  • B 2 . 8 6 Γ— 1 0 βˆ’ 2 eV
  • C 4 . 4 6 Γ— 1 0 βˆ’ 2 eV
  • D 3 . 3 1 Γ— 1 0 βˆ’ 2 eV
  • E 3 . 7 7 Γ— 1 0 βˆ’ 2 eV

Q8:

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

  • A 1 8 . 2 Γ— 1 0 6 J
  • B 4 . 5 5 Γ— 1 0 6 J
  • C 3 . 0 2 Γ— 1 0 6 J
  • D 2 . 6 3 Γ— 1 0 6 J
  • E 1 . 5 1 Γ— 1 0 6 J

Q9:

The separation between hydrogen atoms in a H2 molecule is about 0.075 nm. Determine the characteristic energy of rotation in eV. Use a value of 1 . 0 5 Γ— 1 0 βˆ’ 3 4 Js for the value of the Reduced Planck Constant, and a value of 931.5 MeV/c2 for the value of the unified atomic mass unit.

  • A 7 . 2 3 Γ— 1 0 βˆ’ 3 eV
  • B 7 . 1 1 Γ— 1 0 βˆ’ 3 eV
  • C 7 . 3 2 Γ— 1 0 βˆ’ 3 eV
  • D 7 . 4 3 Γ— 1 0 βˆ’ 3 eV
  • E 7 . 5 9 Γ— 1 0 βˆ’ 3 eV