The ionization energy of a certain element is 412 kJ/mol. When the atoms of this element are in the first excited state, however, the ionization energy is only 126 kJ/mol. Based on this information, calculate the
Interpretation: The wavelength of light discharged in a transition from first state to a ground state is to be calculated.
Concept introduction:
Ionization energy is defined as the energy which is required to remove valence electron from a neutral atom or molecule in gaseous phase.
The ionization energy is expressed in
The wavelength of light is represented as follows:
Here,
is the energy difference,
is Planck’s constant, and
is the speed of light.
Answer to Problem 138AP
Solution:
Explanation of Solution
Given information:
The energy difference between the ground state and the dissociation limit
is equal to
Substitute
for
for
in equation (1) as follows,
In one kilojoule, there are
joule present.
So,
In one mole, there are
So, in
The wavelength of light that is emitted in a transition is calculated as follows:
Substitute
for
in equation (2) as follows:
Since
Therefore,
The wavelength of light discharged in a transition is
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