Each of the statements below attempts to explain why some periodic property varies predictably among elements in the periodic table. Determine if each statement is true or false.

Within a family, elements with higher atomic numbers have higher electronegativity because the valance electrons are in lower principal energy levels.
Within a period, elements with higher atomic numbers require less energy to remove an electron from the atom, because the valance electrons are in higher principal energy levels.
Within a family, elements with lower atomic numbers have atoms of larger radius because the atoms have lower effective nuclear charge.
Within a family, elements with lower atomic numbers require more energy to remove an electron from the atom, because the atoms have higher effective nuclear charge.
Within a family, elements with higher atomic numbers have lower ionization energy because the valance electrons are in higher principal energy levels.
Within a period, elements with higher atomic numbers pull more strongly on electrons in a bond, because the atoms have lower effective nuclear charge.

I will happily critique your thinking, and perhaps argue it out with you.

The statements are as follows:

1. Within a family, elements with higher atomic numbers have higher electronegativity because the valence electrons are in lower principal energy levels.

- False. Electronegativity generally decreases as you go down a group or family in the periodic table.

2. Within a period, elements with higher atomic numbers require less energy to remove an electron from the atom, because the valence electrons are in higher principal energy levels.

- False. Elements with higher atomic numbers generally require more energy to remove an electron from the atom as you move across a period.

3. Within a family, elements with lower atomic numbers have atoms of larger radius because the atoms have lower effective nuclear charge.

- True. Atomic radius generally increases as you move down a group or family in the periodic table.

4. Within a family, elements with lower atomic numbers require more energy to remove an electron from the atom, because the atoms have higher effective nuclear charge.

- False. Elements with lower atomic numbers generally require less energy to remove an electron from the atom as you move down a group.

5. Within a family, elements with higher atomic numbers have lower ionization energy because the valence electrons are in higher principal energy levels.

- False. Elements with higher atomic numbers generally have higher ionization energy as you move down a group.

6. Within a period, elements with higher atomic numbers pull more strongly on electrons in a bond, because the atoms have lower effective nuclear charge.

- False. Elements with higher atomic numbers generally have higher effective nuclear charge and pull more strongly on electrons in a bond as you move across a period.

To determine if each statement is true or false, we need to understand the periodic trends and properties mentioned in the statements.

1. Within a family, elements with higher atomic numbers have higher electronegativity because the valence electrons are in lower principal energy levels.
True: This statement is true. Electronegativity tends to increase as you move across a period from left to right on the periodic table. This is because atoms with higher atomic numbers have more protons in their nuclei, resulting in a stronger attraction for electrons in the same energy level (valence electrons). Therefore, elements with higher atomic numbers (moving down a group) have higher electronegativities.

2. Within a period, elements with higher atomic numbers require less energy to remove an electron from the atom because the valence electrons are in higher principal energy levels.
False: This statement is false. The energy required to remove an electron from an atom is called ionization energy. Ionization energy generally increases as you move across a period from left to right. This is because as you move across the period, the atomic number increases, and the effective nuclear charge (the attractive force between the protons in the nucleus and the valence electrons) increases. Therefore, elements with higher atomic numbers (moving across a period) require more energy to remove an electron from the atom.

3. Within a family, elements with lower atomic numbers have atoms of larger radius because the atoms have lower effective nuclear charge.
True: This statement is true. Atomic radius tends to increase as you move down a group in the periodic table. This is because, as you move down, the principal energy levels (electron shells) increase, resulting in larger atomic size. Additionally, the lower atomic numbers (moving down a group) have lower effective nuclear charge, which means the attraction between the nucleus and valence electrons is weaker, allowing the electrons to be further from the nucleus and contributing to a larger atomic radius.

4. Within a family, elements with lower atomic numbers require more energy to remove an electron from the atom because the atoms have higher effective nuclear charge.
False: This statement is false. As mentioned earlier, ionization energy generally increases as you move across a period from left to right, not when moving within a family (group). Elements within a family have similar valence shell configurations, and their ionization energies decrease as you move down a group due to the increasing atomic size and decreasing effective nuclear charge.

5. Within a family, elements with higher atomic numbers have lower ionization energy because the valence electrons are in higher principal energy levels.
False: This statement is false. Ionization energy tends to decrease as you move down a group in the periodic table, not increase. This is because, as you move down, the valence electrons are in higher principal energy levels and further from the nucleus, making it easier to remove an electron. Therefore, elements with higher atomic numbers within a family (moving down the group) have lower ionization energies.

6. Within a period, elements with higher atomic numbers pull more strongly on electrons in a bond because the atoms have lower effective nuclear charge.
False: This statement is false. Within a period, elements with higher atomic numbers (moving from left to right) actually have higher effective nuclear charge. This means they pull more strongly on electrons in a bond. The effective nuclear charge increases across a period because the number of protons in the nucleus increases. Therefore, elements with higher atomic numbers pull more strongly on electrons in a bond, not less.

I hope this explanation helps you understand the periodic trends and how to determine the accuracy of the statements.