Quantum Chemistry/Example 17

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The force constant of HCl is determined computationally to be 480 N/m. Given this information find the frequency of EM radiation required to excite the HCl molecule from its ground state to its first excited state.

Solution[edit | edit source]

Given the bond constant (k) of HCl , we use the relationship between fundamental frequency and bond constant to find the bond constant.

where is the bond constant.

is the reduced mass of HCl.

To find the reduced mass of HCl the masses of H and Cl are multiplied and divided by the sum of the masses.

For HCl the reduced mass is calculated as

convert to the SI unit of Kg

To find the fundamental frequency

After finding the fundamental frequency, the Energy at different quantum levels can be found by

For the ground state i.e.

For the first excited state i.e.

The difference in energy between the two states is

and Energy is defined as Planck's constant multiplied by frequency