One way to estimate the effective charge
Interpretation: The effective nuclear charge(
Concept introduction:
Ionization energy is the energy needed to remove a valence electron from a neutral atom in gaseous phase.
The ionization energy is expressed in
Across the period, effective nuclear charge increases and down the group, effective nuclear charge decreases.
Answer to Problem 123AP
Solution: The effective nuclear charge of lithium, sodium, and potassium are1.26, 1.84, and 2.26, respectively. The value of
Explanation of Solution
Given information:
The equation for first ionization energy is given as follows:
Here,
Rearrange the above equation as follows:
For lithium, the principle quantum number is 2 and first ionization energy
So, the effective nuclear charge for lithium is calculated as follows:
Substitute 2 for
For sodium, the principle quantum number is 3 and the first ionization energy
So, the effective nuclear charge for lithium is calculated as follows:
Substitute 3 for
Similarly, for potassium, the principle quantum number is 4 and first ionization energy
So, the effective nuclear charge for lithium is calculated as follows:
Substitute 4 for
Down the group, the effective charge decreases because shells with large value of
For lithium, the value of
For sodium, the value of
For potassium, the value of
Since, the
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