which element has a more favorable (exothermic) electron affinity?

K
Mg

how do i determine this?

K has the most energy.

http://en.wikipedia.org/wiki/Electron_affinity

Look at the periodic trend.

To determine which element has a more favorable (exothermic) electron affinity between K (Potassium) and Mg (Magnesium), you can compare the trends in electron affinity across the periodic table and consider their positions.

1. Locate the elements on the periodic table: First, locate both K and Mg on the periodic table. K is found in Group 1, Period 4, while Mg is found in Group 2, Period 3.

2. Consider the trend: Electron affinity generally increases as you move from left to right across a period, and decreases as you move down a group. This is because as you move across a period, the effective nuclear charge increases (number of protons in the nucleus), making it easier for the atom to attract an additional electron. As you move down a group, the electron being added is farther from the nucleus, so the attraction is weaker.

3. Compare the positions of K and Mg: Considering the trend, K is located to the left of Mg on the periodic table, and hence, has a larger atomic radius. A larger atomic radius implies that the valence electrons of K are farther from the nucleus compared to Mg. Therefore, as per the trend, Mg would have a higher electron affinity compared to K.

In conclusion, Mg is likely to have a more favorable (exothermic) electron affinity compared to K, due to its position in the periodic table and the trend in electron affinity.