Use your knowledge of modern atomic theory and bonding to explain each of the following experimental observations. (Your explanations should be specific.) Refer to both substances when comparing. Within a family such as the alkaline earth metals, the ionic radius increases as the atomic number increases. The radius of the bromine atom is smaller than the radius of the bromide ion, Br-1. The first ionization energy of aluminum is lower than the first ionization energy of magnesium.

(1) In the modern day periodic table the atomic size is increasing when we  move down the group and it decreases when we move along the period from left to right. that's why Within a family such as the alkaline earth metals, the ionic radius increases as the atomic number increases. Alkaline earth metals have loosely held electrons which results in its increased size.

(2) The radius of the bromine atom is smaller than the radius of the bromide ion, Br-1 this happens because bromine is a non metal, and it also has a high electronegativity among other group elements as halogen group has high electronegativity. when the bromine acquires one extra electron and forms ion, the configuration of bromine earlier was  but on addition of the electron the p shell will now have 6 electrons resulting in the newly added electron repels the former neutral orientation and as a result of repulsion the size increases.

(3) The first ionization energy of Aluminum is lower than that of the first ionization energy of magnesium   because magnesium has fully filled orbital whereas Aluminum has one electron in the 3p orbitals, fully filled 3s orbitals has strongly held by the nucleus in case of Mg whereas 3p orbitals is shielded from the nucleus therefore it becomes easy to take out 3p electron that 3s electron.  

put the answers   and i could answer.

in the analysis of systems that involve fluid flow, we frequently encounter the combination of properties u and pv.