The ionization energy of hydrogen atom is 13.6 eV and the first ionization energy of sodium atom is 5.1 eV. The effective nuclear charge experienced by the valance electron of sodium atom is __________. (Round off to one decimal place)Correct answer is between '1.7,1.9'. Can you explain this answer?

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Answer

Answer

Explanation:

Firstly, let us understand the concept of effective nuclear charge. Effective nuclear charge is the net positive charge experienced by an electron in an atom. It is less than the actual nuclear charge due to the shielding effect of inner electrons.

The effective nuclear charge (Zeff) experienced by the valence electron in sodium can be calculated using Slater's rule. According to Slater's rule, the effective nuclear charge is given by:

Zeff = Z - S

Where Z is the atomic number (number of protons) and S is the screening constant.

For sodium, the atomic number is 11. Therefore, the nuclear charge is +11.

The screening constant (S) can be calculated using the following rules:

1. The electrons in the same shell do not shield each other.

2. The electrons in the inner shells shield the valence electron from the nuclear charge.

3. The shielding effect of electrons in a particular shell decreases as the distance between the nucleus and the electron increases.

4. The shielding effect of s electrons is greater than p electrons, which is greater than d electrons.

Using these rules, we can calculate the screening constant for sodium as follows:

Screening constant for 1s electron = 0.35 x 2 = 0.70

Screening constant for 2s and 2p electrons = 0.85 x 8 = 6.80

Total screening constant (S) = 0.70 + 6.80 = 7.50

Zeff = 11 - 7.5 = 3.5

Therefore, the effective nuclear charge experienced by the valence electron in sodium is 3.5.

The first ionization energy of sodium atom (5.1 eV) is less than the ionization energy of hydrogen atom (13.6 eV) because sodium has a greater atomic radius and the valence electron is farther away from the nucleus, making it easier to remove.

Answer: The effective nuclear charge experienced by the valance electron of sodium atom is 3.5. (rounded off to one decimal place)

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