Atoms

Step 1: Understand the Periodic Trend of Ionization Enthalpies Ionization enthalpy generally follows periodic trends: - Ionization energy increases across a period (from left to right). - Ionization energy decreases as we move down a group (from top to bottom).

Step 2: Analyze the Given Data From the question, we are given the following values for the first ionization enthalpy of the elements: - Sodium (Na): 496 kJ/mol - Magnesium (Mg): 737 kJ/mol - Silicon (Si): 786 kJ/mol Aluminum (Al) lies between magnesium (Mg) and silicon (Si) in the periodic table.

Step 3: Estimate the Ionization Enthalpy of Aluminum Since aluminum (Al) is in the same period as silicon (Si) and magnesium (Mg), its first ionization enthalpy will be between the values for magnesium and silicon. - The first ionization enthalpy of magnesium is 737 kJ/mol. - The first ionization enthalpy of silicon is 786 kJ/mol. Since aluminum lies between magnesium and silicon, its ionization enthalpy will be closer to that of magnesium, but slightly higher than 737 kJ/mol. A reasonable estimate for the first ionization enthalpy of aluminum would be 575 kJ/mol.

Step 4: Final Answer Thus, the first ionization enthalpy value of aluminum (Al) is:

The acidic strength of these oxides increases from Al O (amphoteric) to SiO (weakly acidic) to P O (strongly acidic) and then to SO (more acidic due to its ability to form sulfurous acid upon hydration).

Step 1: Energy Formula for Hydrogen-like Ion The energy of an electron in a hydrogen-like ion (ionized atom) is given by the formula for the energy levels of hydrogen: where: - is the principal quantum number (for the first orbit, ), - is the energy for the first orbit in the hydrogen atom.

Step 2: Convert Energy from eV to Joules To convert the energy from electron-volts (eV) to joules (J), we use the conversion factor: Thus, the energy for the first orbit is:

Step 3: Adjust for Hydrogen-like Ion Energy For a hydrogen-like ion, the energy formula changes based on the ion's nuclear charge , with the energy being: In this case, the problem provides the radius, and we must use it to determine . The first orbit's radius is related to and through: Where: - is the Bohr radius (the radius of the first orbit in hydrogen). Given the radius , we can solve for : Thus, .

Step 4: Calculate the Energy for the Hydrogen-like Ion Now, we can calculate the energy for the hydrogen-like ion using : Convert this energy to joules: Thus, the energy associated with the first orbit is: