The energy of an electron in a one-electron atom or ion equals (–2.18 x 10 –18 J) (Z 2 /n 2 ). Estimate the ionization energy for the valence electron of the Li atom and compare it to its theoretical value of 520 kJ/mol.

Here we're told that the energy of an electron in a one electron atom or ion equals negative 2.18 times 10 to the negative 18 joules times z squared over n squared, where z is our atomic number and n is our shell number. Here it's just to estimate the ionization energy for the valence electron of the lithium atom and compare it to its theoretical value. Now the theoretical value for the ionization of lithium is approximately 520 kilojoules per mole. Now what we're going to say is that lithium has an electron configuration of 1 s 2, 2 s 1. 2 s 1 represents its outer shell, and therefore it has one valence electron in its outer shell. Here we're gonna use this formula, negative 2.18 times 10 to the negative 18 joules times z squared. Lithium has an atomic number of 3, so that'd be 3 squared, divided by the n value for its valence electron. Its valence electron is in the second shell, so n equals 2. When we multiply this out that gives me for my joules, negative 4 point, and here we're gonna need space to work this out. It comes out to negative 4.905 times 10 to to the negative 18 joules, and here that's for each electron. Here we need to change it into kilojoules per mole, so what we're gonna do now is we're going to get rid of joules, so 10 to the 3 joules for every 1 kilojoule, And then to go from electrons to moles we're gonna say 1 mole of electrons is 6.022 times 10 to the 23 electrons. So electrons cancel out, and what we'll have here is kilojoules per mole. This comes out to approximately negative 2953 kilojoules per mole. Now we can see here that ionization energy is related to the potential energy of the electron, but we can see that their values are quite different. That's because the potential energy also takes into account things such as repulsion from nearby electrons, as well as attractive forces between the electron in the nucleus. These are discussed later on in the periodic trend dealing with effective nuclear charge, and basically the repulsion and the and attraction that exists between nuclei and electrons. So this explains a discrepancy within their values. But just remember, you don't have to memorize the ionization of lithium, you just need to remember the basic trend. As we head to the top right corner of the periodic table, ionization energy will increase.

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10. Periodic Properties of the Elements

Periodic Trend: Ionization Energy

General Chemistry

10. Periodic Properties of the Elements

Periodic Trend: Ionization Energy

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Multiple Choice

The energy of an electron in a one-electron atom or ion equals (–2.18 x 10^–18 J) (Z²/n²). Estimate the ionization energy for the valence electron of the Li atom and compare it to its theoretical value of 520 kJ/mol.

491 kJ/mol

-179 kJ/mol

-1682 kJ/mol

-2953 kJ/mol

-5062 kJ/mol

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Verified step by step guidance

Identify the formula for the energy of an electron in a one-electron atom or ion: \( E = -2.18 \times 10^{-18} \text{ J} \times \frac{Z^2}{n^2} \), where \( Z \) is the atomic number and \( n \) is the principal quantum number.

For a lithium atom (Li), the atomic number \( Z \) is 3. The valence electron is in the first shell, so \( n = 1 \). Substitute these values into the formula: \( E = -2.18 \times 10^{-18} \text{ J} \times \frac{3^2}{1^2} \).

Calculate the energy \( E \) in joules for a single electron using the substituted values. This will give you the energy required to remove one electron from a single Li atom.

Convert the energy from joules per atom to kilojoules per mole. Use Avogadro's number \( 6.022 \times 10^{23} \text{ mol}^{-1} \) to convert: \( E_{\text{kJ/mol}} = E_{\text{J}} \times 6.022 \times 10^{23} \times 10^{-3} \).

Compare the calculated ionization energy in \( \text{kJ/mol} \) to the theoretical value of 520 \( \text{kJ/mol} \) and the given options to determine the closest match.