Explanation:

Metals are elements that tend to lose electrons and form positive ions, whereas oxygen is a non-metal that tends to gain electrons and form negative ions. When metals react with oxygen, they undergo a chemical reaction called oxidation, where the metal atoms lose electrons and the oxygen atoms gain electrons.

a) Across the periodic table:
Metals become more reactive with oxygen as you move across the periodic table from left to right. This is because the atomic size decreases and the ionization energy increases across a period. As the atomic size decreases, the outermost electrons are held more tightly by the nucleus, making it more difficult for the metal atoms to lose electrons and react with oxygen.

b) Across Period 2:
Period 2 of the periodic table consists of the elements lithium (Li) to neon (Ne). Among these elements, metals such as lithium, beryllium, and sodium are less reactive with oxygen, while magnesium, aluminum, and silicon are more reactive. The reactivity with oxygen increases from left to right across the period.

c) Down Group-II:
Group II of the periodic table consists of the elements beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra). As you move down the group, the reactivity of metals with oxygen increases. Beryllium is the least reactive metal in this group, while radium is the most reactive. This is because the atomic size increases down the group, leading to a decrease in ionization energy. The outermost electrons are further away from the nucleus and are less tightly held, making it easier for the metal atoms to lose electrons and react with oxygen.

d) Up Group-II:
Moving up the Group II elements, the reactivity with oxygen decreases. This is because the atomic size decreases and the ionization energy increases up the group. The outermost electrons are held more tightly by the nucleus, making it more difficult for the metal atoms to lose electrons and react with oxygen.

In conclusion, metals become more reactive with oxygen as you move down Group II of the periodic table. This trend can be explained by the decrease in ionization energy and the increase in atomic size down the group.